must and have to are the same concerning necessity
i must help mum clean the house because she is tired.
i have to help mum clean the house because she is tired.
in obligation: must is used when this obligation is external; i must do this work, or the boss will be angry.
have to is used when the obligation is enternal: i have to do my homework before i go to the club.
ought to= should when used to give advice, but should is widely used:
you ought to do your homework.
you should do your homework.
need to expresses necessity to: i need to clean my house before i go out.