You don't want this girl. Respect yourself enough to admit that she is bad news. It's no longer a question of what to do, but how to do it. You're obviously kicking her a$$ to the curb, no question. Now it's just a matter of logistics.
You bought or are renting this house? If you bought..well, you're going to need to set that straight. If you're renting try to find a buddy who is looking for a place, obviously pending on whose name is on the lease.
If it were me, I would send her a message on FB saying things aren't working out and you no longer want to continue said relationship. She's cheating on you, decency no longer matters. Either you move out or take her sh*t and put it on the curb.