Hey Redlocks,
What state are you in? Different states have different rental laws; if you're lucky you have tenancy-at-will where you have to give 30 days' notice and you can just boot them, even if they are ojn a lease.
Do you have a written agreement that you can look at and find violations of it?
Do they make noise that violates town bylaws? That in itself could be grounds for eviction.
I'm a landlord myself and have friends who are landlords- I've been reasonably lucky; the worst things that have happened so far is I got bitten by a tenant's dog, I've had damage problems, and one guy whose checks bounced EVERY month. But the stories my neighbor has- OMG, he was trying to evict one tenant for nonpayment and she took him beofre the board of health for imagined violations. So he had to have her put rent in escrow while they did inspections (which totally cleared him of any wrongdoing, it's an awesome apartment and I want to move in there!). Meanwhile he was having a tough time paying bills because as you know mortgages on a multi are based on rental income!!! Yikes.
Best of luck kicking them out.
My advice is get anything OUT of your house temporarily that you wouldn't want the cops to see, issue a formal eviction notice through the courts, sit back, and enjoy the show.
I hate disrespectful neighbors.