To muck up the waters further, AHD includes both plural forms without indicating a preference:
e·de·mas or e·de·ma·ta (-mə-tə) also oe·de·mas or oe·de·ma·ta
https://ahdictionary.com/word/search.html?q=edema

Actually, MW does contain information lower in the article:
edema
noun ede·ma (Medical Dictionary)
plural ede·mas also ede·ma·ta \-mət-ə\
http://www.merriam-webster.com/dictionary/edema

Bei kurzer Durchsicht von PubMed habe ich (Nicht-ENS) festgestellt, dass zahlreiche Verwendungen des Plurals "edemas" von Nicht-Muttersprachlern stammen.
Hier ein Nachweis zu einem Fachartikel von vermutlich muttersprachlichen Autoren:
The data suggest that the edemas result from interaction of the products of the cyclooxygenase and lipoxygenase pathways of AA metabolism.
http://www.nature.com/jid/journal/v80/n1/full...

Ich bin zwar kein ENS, wundere mich aber sehr, daß Ödem ein mass noun oder uncountable sein soll.

Jedenfalls gibt es diverse wissenschaftliche Texte aus UK, hauptsächlich mit der Pluralform oedemas.
https://duckduckgo.com/?q=oedemas+site%3A.ac....

Using a google book search, I found both edemas and edemata in technical books, and I didn't sense that the choice depended on the author being an NES or not.

Ich bin zwar kein ENS, wundere mich aber sehr, daß Ödem ein mass noun oder uncountable sein soll.

Im Deutschen sagt man: "Ich habe ein Ödem", im Englischen: "I have oedema" NICHT: "I have AN oedema".

Hm, das scheint eine Entwicklung jüngerer Zeit zu sein:

https://books.google.com/ngrams/graph?content...

Aber meine Einschätzung ist da nur marginal von Bedeutung. Vielleicht schaut ja z.B. Marianne BE vorbei, die müßte das besser beurteilen können.

Ich würde das Wort "oedema" so wie "stigma" behandeln und für den Plural beide Formen angeben: "oedema - oedemata" (or: oedemas) wie "stigma - stigmata (or: stigmas):

stigma
plural stig·ma·ta or stigmas
(s. Merriam-Webster)

Im Deutschen würde man sich wohl scheuen, von "Stigmas" od. "Stigmen" zu reden. Bei diesem Wort ist die (korrekte) griechische Pluralform der neutralen Substantive mit der Singularendung auf Alpha üblich. Der Begriff Stigma (altgriechisch στíγμα, Mehrzahl Stigmata) bedeutet wörtlich „Stich-, Punkt-, Wund- oder Brandmal“.
(s. Wikipedia)
Bei "Thema" ist das schon anders. Da gibt's den schönen Witz unter Altphilologen: "Was ist das heutige Themata?" :-)

Ich bin kein ENS, aber ich hab mal online in das entsprechende Kapitel im Harrison geschaut: http://accessmedicine.mhmedical.com/content.a...
Dort kommt ein Plural nicht vor, und googeln mit oedema(s) + BMJ gibt keine Treffer für oedemas, aber einzelne für edemata und oedemata.

In medizinischen Texten habe ich diesen Plural allerdings noch nie gesehen. Dafür findet sich in der deutschen Übersetzung dann oft das Ödem, wo es die Ödeme heißen müsste

English nouns ending in -ma are derived from neuter Latin nouns of Greek origin.
edema / oedema
stigma
derma
lemma
parenchyma
plasma

The Latin genitive singular ending is -atis, & the Latin nominative plural ending (when there is one) is -ata

As English nouns, some of these are treated as mass nouns or uncountable nouns without a plural in some (possibly even most) contexts.
edema / oedema
derma
plasma
parenchyma

However, in other contexts, it may be necessary to distinguish between different types of edema (caused by different factors) or different types of derma or plasma or parenchyma (resulting from different origins or with different physical structures or properties). In these latter contexts, a careful writer will use a phrase like "types of" (before the word) to make the distinctions, but it is also possible to make the word plural.

In forming the plural, one option is to treat the word as Latin & use the Latin plural ending:
edemata / oedemata
stigmata
dermata
lemmata
parenchymata
plasmata
This option may be looked upon as erudite, scholarly, or other less generous descriptive adjectives.

However, if the words are truly accepted as English words, then the other option (& the one I prefer) is to use the standard English plural ending:
edemas / oedemas
stigmas
dermas
lemmas
parenchymas
plasmas
This option is more casual, colloquial, & reader-friendly.

At least that's my opinion. In the Latin names of plants & animals, there are many more such endings similarly declined (-nema, -paegma, -stemma, -zema, -stelma, -stroma, -phragma, -uma).

Botanical Latin: History, Grammar, Syntax, Terminology and Vocabulary, by William T. Stearn (Hafner Publ. Co., 1966), p. 82

Unterstützung für #8.
Ich habe eine ähnlich Suche für das New England Journal of Medicine durchgeführt.

Suche: oedemas OR oedemata OR edemas OR edemata site:nejm.org
https://www.google.at/search?hl=de&as_q=&as_e...
Resultat: 2 Artikel, beide älter als 90 Jahre, und eine Buchrezension von 1989. Der Autor des Buches wird in zwei Tagen 79 und hat edemas vermutlich aus alten Publikationen übernommen.

Zum Vergleich: oedema OR edema site:nejm.org
https://www.google.at/search?hl=de&as_q=&as_e...
Resultat: Hunderte Fundstellen.

Mein Fazit:
Wenn zwei der besten englischsprachigen medizinischen Fachzeitschriften (hohes Ansehen, striktes peer review, aufwendige redaktionelle Bearbeitung) den Plural offensichtlich nicht (mehr) verwenden, dann sollte zumindest ein [arch.] oder [obs.] zum Eintrag gesetzt werden.

Weiterer Hinweis: Fast alle angezeigten Fundstellen in Pubmed (http://www.ncbi.nlm.nih.gov/pubmed/?term=%22e...] ) sind entweder fremdsprachig (Beispiel: Spanisch - http://www.ncbi.nlm.nih.gov/pubmed/24636598 ) oder stammen vermutlich nicht von ENS (Beispiel: Serben - http://www.ncbi.nlm.nih.gov/pubmed/24502104 ).

OP: Unsere Vermutung ist, dass die Pluralform im fachsprachlichen Kontext verwendet wird.
Diese Vermutung ist nicht zutreffend, zumindest was ENS angeht.

I consider edema to be a mass noun and was unaware that there was a plural.

In my opinion, edema is used like swelling, without a plural:

My grandmother had edema.
The swelling was most visible in her legs.

*My grandmother had edemas in both legs.
*The swellings in her legs could be bothersome at times.

I am not any kind of an authority, but based on my language sense as a native speaker, I would guess edemata would be a believable plural for medical texts. It "sounds" right in a field that draws more heavily from Greek and Latin forms. By that I don't mean that medical texts do use a plural, I am simply saying what would sound right based on my fallible judgement as a native speaker.

Just my 2p:
“Oedema” these days is commonly treated as an uncountable, and I think that most UK medics use it that way in both speech and writing. Like Doris, I would never say “the patient has AN oedema” (but then I wouldn’t say “the patient had A surgery”, either, even though it’s apparently not only acceptable but commonly used in AE). Which means that I would tend to use, for example, “types of primary/secondary oedema” rather than “primary/secondary oedemas”, although theoretically the latter would be possible.

Re the forms “oedemas” and “oedemata”: the dictionary entries indicate that both forms are valid but, like hhberlin and unlike wienergriessler, I don’t have the sense that the choice depends on being an NES or not. On the contrary, the 10 entries found in PubMed for “oedemata” are all from non-NESs. (In Google books, you have to be careful of references to Atys oedemata and purely Latin texts.) I think it is more to the point that there are relatively few occasions on which native English speakers actually use a plural form at all.
 
Checking the BMJ journals archives (from 1840 available online) there are only 170 uses of “oedemas” (from 1880 to the present) – many of the more recent examples are from non-NESs, while early/mid-20th century references are from articles by NESs ) – and merely three of “oedemata” (1906, 1909, 1962). There are also 34 examples of “odems”, which I would take to be proofreaders’ oversights. During the same period, there are 41,099 hits for “oedema”.

In summary: even tho’ plural forms are possible and have been legitimately used in the past, non-NESs still tend to use a plural form when an NES would use the singular (mass noun). While it would be valid for LEO to give both plurals for sake of completeness (with “oedemas” rather than “oedemata” being the default form), I think the common usage as an uncountable needs to be emphasised strongly.

Usage in the Journal of the American Medical Association:
https://www.google.com/?gws_rd=ssl#q=%22oedem...

Examples:
Cerebrospinal Fluid and the Brain Edemas
Excluded from consideration are the nutritional edemas, the nephritic edemas, the cardiac edemas and the edemas of pregnancy; […]
The Antiedemic Actions of Calcium in Experimental Irritative Edemas
Acute mountain sickness and the edemas of high altitude: A common pathogenesis?

Also, FWIW:
https://books.google.com/ngrams/graph?content...

Agalinis's posts in #9 and #13 say just about everything I would have wanted to say.

Especially the examples in #13. I can imagine someone using 'edemas' like that in a medical textbook to mean different types or classes of edema, just as other words that normally have only one form could be plural in that context. ('This chapter discusses the pneumonias.' 'Those medicines are effective only in certain leukemias.' Or indeed, as we've discussed elsewhere with species names: 'This chapter discusses the salt-water fishes / grasses.') I'm not sure if LEO actually has an overall policy for that global distinction, or if (as I suspect, and as seems reasonable) it just suppresses that entire category of exceptions and lists the usual plural form bzw. null plural.

I can imagine someone 100 or 200 years ago, when all doctors still used Latin, using 'edemata' in a similar context to mean types or classes. But today that form would make me suspect a non-native speaker, even if it's still listed in dictionaries and is perhaps not technically incorrect. If it were included in LEO, I would suggest a marking like [rare or obs. also:].

We all agree that in the vast majority of contexts, 'edema' is a noncount word. 'The patient has (a little, some, a lot of) edema in one or both legs.'

Of all the examples in #9, as far as I know, the only plural in -ata that's really used is stigmata., and only in the specific meaning of the wounds of Christ. (That is, people talking about social stigmas use the English -s plural.)

OT @Marianne:

This is all in the archive somewhere, but again for the record: I apologize for the many AE speakers who use 'a surgery' when they ought to use 'an operation.' They're obviously in a large and growing majority, but as with those who use 'lay' when they ought to use 'lie,' they're still mistaken. (IMHO, from the standpoint of careful use of language, which is necessarily prescriptivist within reason, etc.) I continue to believe, or perhaps hope, that there are still quite a few AE speakers who use 'surgery' correctly, only as a noncount noun. ('He had knee surgery.' 'He had a knee operation.' 'The rate of knee operations is increasing.')

zu #9:
In forming the plural, one option is to treat the word as Latin

Das ist so nicht richtig. Alle diese Wörter sind griechisch, nicht lateinisch. "derma" z.B. gibt es nicht in der lat Sprache; auch keinen Genitiv *dermatis. "Haut" heißt "cutis" od. "pellis" (vgl. med. Sprachgebrauch "subcutan"oder "Pellagra").

zu #15:
Agalinis schrieb: treat the word as Latin
So viel ich weiß, wird in der Zoologie bei aus dem Griechischen stammenden Begriffen die lateinische Grammatik angewandt (zumindest in der zoologischen Nomenklatur).

That is correct, Wachtelkönig.
Scientific Latin (for science is the source of the words discussed here, whether the science is physics, chemistry, botany, zoology, medicine, or whatever) "is best described as a modern Romance language of special technical application, derived from Renaissance Latin with much plundering of ancient Greek, which has evolved, mainly since 1700 and primarily through the work of Carl Linnaeus (1707--78), to serve as an international medium for the scientific naming of plants [and animals and chemicals and physical particles and physical principles] in all their vast numbers and manifold diversity. […]
"The general effect of all this has been to make [scientific] Latin autonomous. It is now as unintelligible to classical scholars as modern English would be to a Frenchman who had learned only Anglo-Saxon. […]
"The relation of [scientific] Latin to classical Latin is that of a former dependency which by vigorous economic growth over many years has established traditions and divergencies arising out of its special conditions and history that must be accepted, if need be, by proclaiming its status as a language in its own right."

From the same source as cited earlier, Botanical Latin by William T. Stearn

Or, if you prefer, this quote from Karl Vossler (which I only know in English translation, The Spirit of Language in Civilization, 1932):
"Science castigates and enriches, conserves and accelerates, prunes and sharpens, obstructs and drives forward linguistic thought in the service of the logos, which it rapes, deprives of its naiveté and enriches instead with innumerable children."

Thus, the origin of edema (from Merriam-Webster):
New Latin, from Greek oidēma swelling, from oidein to swell

Also, the derivative adjectives:
edematous
edematose

Apart from the words listed by Agalinis in #9, there are many terms used in medicine with similar Greek via Latin derivations where “-ata” plural forms have been used in the past, even if now replaced by the simple “-s” form, e.g. many of the words ending in “-oma”.

Some have been dealt with as follows:
stoma pl.: stomata, stomas artificial opening [med.] -- das Stoma Pl.: die Stomata
sarcoma pl.: sarcomas, sarcomata [med.] -- das Sarkom auch: Sarkoma Pl.: die Sarkome

However, the LEO dictionary makes no mention of the “-omata” plurals on the English side for
adenoma
carcinoma
condyloma*
haematoma
lipoma
neuroblastoma etc.

Again the modern plural of “-omas” should in some way be emphasised, but “-omata” still appears in dictionaries (I can hunt up references, if required) and has been used in many texts in the past. (I don’t know which plural is more common for plants these days so "stomata" may still be the default in botanical terms if not in medical – Agalinis would know.)

* condylomata is still commonly used

OT @hm--us:
No need for you to apologise - in no way do I hold you responsible ;-)

In the botanical sense, stomata is regularly used today.

However, alternative forms, stomate (singular) & stomates (plural), enjoy periodic popularity. The problem with alternative forms is that, although the pairing should be:
stoma / stomata
stomate / stomates
I occasionally encounter papers where the authors use:
stoma / stomates
stomate / stomata
Which makes me wonder, where was the editor of that journal?
https://books.google.com/ngrams/graph?content...

In the botanical sense, they are not artificial, but natural structural elements on the undersurface of a leaf. They allow air to pass into the leaf so that carbon dioxide comes in contact with the chlorophyll-bearing cells & so that surplus oxygen can be expelled. The price for that is water loss. The "guard cells" that form each stoma regulate water loss by swelling & shrinking due to osmotic pressure, causing the stoma to close & open, respectively.
http://en.wikipedia.org/wiki/Stoma

We're straying off-topic from Doris's request.

If I could attempt a consensus response:

Yes, edema / oedema do have plural forms, both of which are rarely used by careful writers today:
edemas / oedemas = preferred
edemata / oedemata = so rarely used today that they might be marked as historical or archaic

Hopefully, Doris can reduce that to a Dictionary entry.

Objections?