Can you legally kick your 21 year old child out of the house in Ohio or do you have to evict him?

Is their name on a lease or deed? If yes, then you have to evict. If not, you are the "king of the castle" and can determine who stays and goes. The police WILL enforce it. I've had a few tenants whose druggie kids moved back in temporarily and then refused to leave and the cops WILL get them out and tell them to make arrangements to get their "stuff" later.