I assume that "him" is the parents' son and that you are trying to detail a situation of continued prohibition. I think that this is what you are getting at. Then 1. and 2. convey the same meaning: The parents prohibit the son from "staying out late".
The difference is that in 1. can mean that the son asks each time he wants to stay out late, and each time his parents so no. 2. can mean that the parents told him once and that is the rule. No questions asked.
Number 3. does not have this meaning. It sounds like you are saying that the parents do not command the son to stay out late. I think what you mean to say is
His parents won't tell him that he can stay out late.
This has the same meaning as the other two. But it could also be interpreted as they allow him to stay out, but they simply don't say it. Maybe they give hints, or don't punish him and ignore it if or when he stays out late.