I would have felt extremely uncomfortable with someone ignoring my 'no' and having suspicious sounding issues afterward.
He has legs, he could have walked somewhere. Just because his car wasn't working didn't mean he gets to stay.
A therapist can help you learn to repeat yourself without exploding. Assertiveness means that your 'no' means 'no' whether the other accepts it or not. "I'm sorry your car isn't working, your phone isn't working, and it's snowing. I'm not up to company so you will have to leave now." Repeated until he leaves or you have to report him for tresspassing.