würde ich sagen

"strained atmosphere"
"fractious atmosphere"

Vielen Dank für die Vorschläge!

Ja, und allerlei Stimmungen können in the air sein ("in der Luft liegen").

There was acrimony in the air, usw.

(An air of tension, glaube ich, würde eher ein Individuum beschreiben: He had an air of tension about him.)

Air of tension would work here just fine.

Where? We do not really have a sentence to work with. There is only harambee's made-up sentence:

"Innerhalb dieser Gruppe (gab es) erhebliche atmosphärische Störungen."

There was a considerable air of tension in this group.

Do you really feel air of tension works well there?

The Oxford English Dictionary has several entries under air that are close in meaning to this, but the one most-specifically related says:

"With qualifying adjective or of, expressing the personal quality, emotion, or impression conveyed by a person's manner."

A few of the examples it provides include:

1962, S. Wynter, Hills of Hebron: "He would deal with Moses as his teachers at school had dealt with him—the stony silence, the air of grim judgment."

1983, A. Bleasdale, Shop Thy Neighbour "Moss has the desperate air of a man no longer in control and no longer caring."

1999, R. Deakin, Waterlog, "They suddenly appeared from nowhere, bearing down on our little unofficial combo with a determined air."

Yes, I really do.
If you google the phrase, "an air of tension in the room", you find that many others agree.
m-w.com definition 4b is, "a surrounding or pervading influence: atmosphere", which brings us full-circle back to the weather allusion.

If they are not necessarily in a room, googling the phrase "air of tension" and the word group finds numerous examples of an air of tension among groups of people.