I have a renter living in my property that invited someone else to stay for awhile. She has repeatedly asked this person to leave, but he has refused. I want to evict him. What is the procedure for Oregon?

Have you ever accepted any kind of payment from him?
How long has he been there?
If relatively short term, e.g. he has no mail or bills sent to him there and hasn't established much in the way of belongings there, you can have him escorted off the premises as a trespasser. But if he claims any kind of tenancy, you have to give written notice to vacate and then follow through with eviction through your local court.

Actually this is not your problem, unless your with your renter says something about the number of occupants.

This person is either the renter's guest or a subleasee. In either case it's the responsibility of the renter to get rid of them.

Yes, your renter has allowed them there, so it is not your issue, (unless you want it to be)

Your renter can give them notice and will have to take them to court to evict them. Consider them a sub renter to the renter.