I need to know what kind of law there is to have a 20yr old kicked out of the house.

Pack his bags, give him 10 bucks and his walking papers and tell him to hit the road. The law, if you are his mom, is just doing it.

Are you a parent, are you a landlord, are you a neighbor who just does not like him?

Assuming you are a parent, legally you have to give him notice and take him to housing court if he does not move out.

I would say that if it is your house and they aren't abiding by your rules you can tell them to leave right now, its not like it's snowing up there right now. Tell them to join the coast guard or something.
I don't know about housing laws with your own kids, that is a bit crazy.. but by all means check the Michigan family law statues to be sure there is nothing like that out there. I am from Michigan and I have never heard of such a thing unless you have a contract with the person for rent.