Can you trust him to be honest with you? Would he tell you if he had an intimate relationship with someone else?

While he is still in the house and you see him regularly, you can have some idea whether he has been with someone. If he has moved out and you haven't seen him for a week, he will have compartmentalized it and you won't have a clue.

So, no joke, if he moves out, do not have unprotected sex with him again. If he comes back, and swears he never had sex with anyone else, and you believe him, then whether he gets checked for STD's is up to you.