It's awkward, two people together in the tower who have absolutely no sense of shame.
It is clearly not awkward for the God of Thunder and his companion, who are just as happy as hell. It's funny for awhile, the way Thor will just pick her up and carry her away mid-conversation, or the way she'll climb him like a tree and steer him out of the room. It's less funny when Tony can't sleep because he can hear them banging from three floors away, which, while a very impressive feat, isn't exactly how he'd like to spend his nights.
At least Thor has an excuse; certainly things on Midgard aren't the way they are on Asgard. For all Tony knows, this is young love for him- he has, however, been known to use the "ignorant alien" thing for all it's worth, so Tony has his doubts.
Natasha's excuse, as far as Tony can tell, is that everybody is too scared of her to say something but Clint, who is endlessly entertained. It is a very effective excuse.
One morning, as Natasha does the Stride of Pride wearing nothing but a cape and a thong, Tony thinks that maybe he should actually make some rules about this kind of thing.
Then he lays down and has JARVIS take his temperature. Something is wrong with all of them.