We use have to to talk about all kinds of obligation. It can be used in all tenses
We also use must to talk about obligation. The meaning is similar to have to, but must is usually used when the speaker sees something as a personal obligation.
We can use need to to talk about things that are necessary. It can be used in all tenses.
No obligation / no necessity
We use not have to when is no obligation to do something.
We use not need to when is not necessary to do something.
We also can use needn't + infinitive without to to say that it is not necessary to do something.
Prohibition
We use mustn't when there is an obligation not to do something. It is mandatory that you do not do something.
Advice
We use should / shouldn't to give advice or to say what we think is the right thing to do.
We can also use ought to / oughtn't to to give advice.
We can use must and have to to give strong advice when we think it's very important that someone does something.
