Obligation

1.- Have to / Must

Similar but a bit Different

• I have to finish my homework. If not my mother won't let me go out. (Obligation)
• I must finish my homework. I don't want to stay at home all they long. (Feeling)
• People under 18 must wait in the other room. (Sign)

If you hesitate or doubt, use have to. It is always correct!

2.- Don't have to / Mustn't

Be careful, here meanings are totally different:

• I don't have to finish my homework today. I still have time till the end of the month. (There is no need)
• I musn't finish my homework today. The teacher didn't give us permission.
• You musn't drive a car if you are under 18. You are not allowed by law.
• Passengers must not smoke in the cabin. It is forbidden by law.

3.- Must / Should

• You must finish your homework today! It's a command.
• If you go to Paris, you must visit the Louvre. You cannot miss it!
• You should finish your homework today, if so you can go out! It's a recommendation. You are giving advice or opinion.

4.- Shouldn't

•  You shouldn't eat so many sweets.- That's my opinion but ... I wouldn't do that. I think that's not ok. That's not correct.

Advice

1.- Personal Opinion.- Are you tired?  Maybe you should go home and take a rest.

2.- Objective Opinion.- Ann, look at your face. You ought to go home and take a rest.

 Permission

1.- May I go in?

2.- May I erase the blackboard?