First off, the gifts and sex could be guilt. Until it's out in the open, she may be more affectionate, until a point comes where she feels she's cheating on OM with you, then she'll back off.
I would confront her with what you know. But before you do, here's the possible result: She'll be remorseful. Maybe even say it was a mistake and that it was something that just happened. She may try to downplay it. She'll tell you it was just a symptom of a bad marriage (you probably should avoid the urge to point out how well things have been between you). Once the cat is out of the bag she'll have two options: leave you for him (or them) or give up these other guys. I'd be prepared for the former possibility. So, you could continue on as though this isn't happening until a time comes when the relationship with some other guy is strong enough to overcome her fear of leaving, or you could draw your line in the sand that you aren't going to be second to anyone. I'd take the latter stance.
You cannot be lonely if you like the person you're alone with. Dr. Wayne Dyer