After getting divorce, my ex husband and I had a on and of relationship and I've being living in his house with my son for 17 years. He did not move back with me because his job is out of the United states. Now he wants me to move out of the house without complying with our verbal agreement of him covering the cost of renting or buying another place.
Is there any thing I can do?

To you have any proof of the verbal agreement. Is there anything in the divorce agreement?

With no legal claim on the house you are a tenant and can be evicted like any tenant.