I think that has happened to almost everyone here. It is kind of a common thread here.
What you need is a way to prove it, without proof you can't really do anything. I have cameras outside all the apartment doors. The other day I was having a look and caught a guest having an unauthorized visitor at 4am. Cameras are very handy. I have wireless ones, I have a few diferent models, but my favorite is the one that looks like a lamp, because you can plug on regular lamp sockets. They only record when there is movement so it is pretty easy to check.
If you cam prove, contact airbnb and ask them to charge for the extra guests.