Obligations

Positive obligations for the present, future or in general:

Stronger:
You have to put on your seat belt. (US)
We are going to/will have to go through the customs when we arrive in New york. (future)
She must put on her seat belt. (UK)
Members shall follow the club rules. (formal/legal/religious/moral codes in writing)

Weaker:
You should take off your shoes in their house.
You ought to take off your shoes in their house. (UK)

Negative obligations for the present, future or in general: Stronger:
You cannot drive without your seat belt on. (US)
You must not drive without your set-belt on. (UK)
Thou shall not kill. (formal/legal/religious/moral codes in writing)

Weaker:
You should not enter their house with your shoes on.
You ought not to enter their house with your shoes on. (UK)

Positive obligations for the past:

Stronger:
We had to go through the customs when we came from the US to Belgium last week.

Weaker:
You should have taken off your shoes when you entered their house yesterday evening.
You ought to have taken off your shoes when you entered their house yesterday evening. (UK)

Negative obligations for the past:

Stronger: 
The waiter could not serve beer to my 17-year old cousin when we were in the US last year.  (US)

Weaker:
You should not have entered their house with your shoes on yesterday evening.
You ought not to have entered their house with your shoes on yesterday evening. (UK)

Lack of obligations for the present, future or in general:

You do not have to take off your shoes when you go through the security check at the airports in Europe.
You are not going to/will not have to take off your shoes at the security check in Zaventem airport when you arrive there. (future)

Lack of obligations for the present, future or in general:

We did not have to take off our shoes when we went through the security check at the airport last week.

I am hereby making some exercises on have to vs. must and should along with the key available.