Whether it seems like it or not, sounds like you got yourself a tenant :).
They say "possession is 9/10ths of the law". What does this mean? It means if I forget to lock my rental unit, and Charles M. Bum III moves in and starts living there.... I can't just grab him by his potato sack and throw him out. He has rights now, he's IN there!! I'd have to go through an eviction process, he never paid rent, never made an agreement, but he's living there now.
Long story short, I'd recommend preparing for this problem by talking to the local Sheriff's Office or Other folks at your courthouse to find out the procedures and get the forms for such a thing. In Wyoming, you can forcibly remove (done by Sheriff) someone in about 2-3 weeks after original eviction notice is given. But it varies state to state and could take up to even 2-3 months depending on your location and situation. So be prepared for that, it could happen.
Now in most deals, part of the contract is to deliver possession (typically) at closing, this means with no bums, no sellers, etc. in the house. This is typically a seller responsibility. However, this means your only choice could be to back out. You also might need to be concerned about them being BAD tenants, they could do damage before you actually get them out. I'd be careful how you proceed and also advise a couple calls to some local attorneys, have them review the contract to see what your options are and advise you of the local statutes on landlord-tenant law and eviction procedures.