Should I tell my co-worker to stop talking to me?
Why do you want to stop talking to this coworker?
He makes me uncomfortable asking for personal details
Normal people talk with their coworkers but if they act weird you should not have to. It is odd they would ask so many questions you can go to HR if they don't stop.
I just canceled it with him
Thats good. Just be sure you set boundaries so that they know what isn't okay to be discussed with you. Otherwise they might not get the hint and persist in asking you personal questions.