I asked a non-sexual girlfriend if she wanted to stay with me a year ago... she agreed to help with costs... I have a monthly agreement with my land lord with no lease and I am the only one who is supposed to be there.. NO MONEY has ever been paid to me and the relationship is strained at best... I now want her out and she won't leave... says I have to serve her papers... what is THE LAW in this situation?? I want to do this right the first time

She is correct, she is a resident and you must evict her. Call your local court house and ask for help with the paperwork. It may cost you $85 but it will get her out. Don't change locks or do anything else in the meantime to avoid giving her valid reason to go after you in court.

Yep, you have allowed her to establish residency. Whether there is a written agreement or not. On the other hand, without an agreement you need nothing more than to give her 30 days notice to move out or you start eviction proceedings. Ask he if she wants an eviction on her credit report?