My roommate and I had a falling out, and he said he filed an eviction for nonpayment after I have already moved out. He is saying that I owe him money that I do not. I paid cash and have no lease. Can he do tis?

Sure he can try... he might even win... but there is no guarantee that he will, because he will have to convince a judge the debt was real and valid. Hard to do without a paper trail.

A lease is not required to be binding. If your roommate can show that you were making monthly rent payments then you were required to give him sufficient notice before vacating. If you just up and moved out without notice, then you owe him rent.

He can't file for eviction since you already left, but he can sue for unpaid rental and win.