Tenant had a lease but it expired 1 year ago. He pays monthly rent. He told me verbally that he was leaving the house the 9th of next month. When I went to the house to see if there were any damages, his father did not let me in. He said that since they had paid this months rent that they were the owners. Not me. That I could not see the house until the 9th. I have their deposit on my possession. They pay the rent every 1st day of the month. Today is the 23rd. I want them out by the first and want to subtract from the deposit any damages to the house. What legal steps do I need to take to get them out of the house the 1st?

Do you have a written lease? What does it say: 1) about your right to inspect; and 2) about damages (reasonable wear and tear excepted, right?) and your right to retain the security deposit?
You need to know the law of your state with regard to these matters; consider retaining an attorney.

Normallyy with a 24 to 48 hour notice they have to let you in to inspect the home. If they are in the home after the first they will have to pay for May rent. You do not give any deposit back to their are completely moved out and you then do a final inspection.

At this point if you did not give them a notice to be out by the first, and they are paid in rent for this month, you have to wait till the 1st and if they are still there give them notice to move, or get the rent for May. And/or both if you are giving them notice to more out by the end of may.

If they stay till the 9th, you hold them liable for mays rent, that is very simple