Before you go changing locks, you might want to hire an attorney. There is law in Ohio that governs "such" relationship, which are typically landlord-tenant relationships, but might not be strictly construed the way you'd prefer. In a classic landlord-tenant relationship, it is illegal to change locks on a tenant, and if you want a tenant booted out, you have to go through the court process and get the court to order an eviction (carried out by the sheriff). A landlord-tenant relationship need not involve a written lease, all that matters is having an agreement. On the face of it, it looks to me as though you agreed to let your son live there, and his attorney would no doubt point to whatever benefit you received from allowing your son to live there as "consideration" in this verbal (vague) contract. The exact terms of that contract don't matter: what matters is that state law limits what you can do. You can read ORC here on the topic of evictions. Actually physically removing a person is a crime (battery), so definitely don't do that. Lockouts have been illegal since 1973. You no doubt can show the court that your son is now effectively a trespasser, but he clearly did not break in without permission, so the bottom line is probably a visit to the court (unless a letter from the attorney resolves the matter).
Alternatively, it could be simpler and cheaper to just go directly for the court process. There are professionally-written manuals for about $20 that spell out the procedures, and an attorney is not actually required to evict someone. You can just treat the situation as a standard landlord-tenant process, give the required notices (using legalese in a notice may well be sufficient). If you do have to file in court, there are a couple hundred bucks of fees associated with filing.
It takes time. There is a 3 day notice requirement on your notice, after that you can file the complaint and a hearing is scheduled after that (county dependent: I hear it's about 3 weeks in Franklin). Defendant can stretch that out for a week or so by asking for a continuance to seek legal counsel, but eventually you will prevail unless the judge is too warm-hearted and orders family counseling (you never know, these days). They you apply for the "red tag", the bailiff posts it within a few days, and that gives him 5 days to leave. If that doesn't work, you call the bailiff for the physical removal, and they probably respond within a couple of business days.