With all respect to everyone's expertise here, but I still think it sounds awkward (even without the "sexual" aspects). Googling for "I don't have enough experience with him,"
I get a whopping 18 hits, most of them apparently from gaming platforms like this one:
Yoda might be more effectiv (sic) than Ashoka, but I don't have enough experience with him to say for certain.
I get even fewer hits (10) with "her" in it, some of those with sexual context: ... especially paired with the sexual withdrawal, and I don't have enough experience with her to know if she'd ask about it if it bothered her.
At the very least the conclusion I come to is that it's not a very common phrasing. To me personally, it's still inherently awkward.
Also, I get even fewer hits using #3's "of" instead of "with": 2 for "him" and 1 for "her." One example: Ah well I don't have enough experience of him, but would you say Sal was first and Larsen after?