(American English) "Must" and "Have to" - No choice. This has to happen. Soldiers have to obey their superior officers' orders. Soldiers have to obey their superior officers' orders. "Shall" - Will (do, say, etc) in the future. This isn't often used in contemporary English. Instead, you usually see it in the Bible, in Shakespeare or in poetic speech/music. We shall overcome (the song) "Ought" - This is what should happen or should have happened. Can say "should" or "should have". Not used often. - He said "They is" when he ought to have said "They are". (or, He said "They is when he should have said "They are") - She played games when she ought to have done her homework (She played games when she should have done her homework.)

I can give you my perspective as a native speaker of American English. Someone else will have to give you his/her thoughts from the perspective of a British English speaker. In modern American English, "must" and "have to" are synonymous. They both imply an absolute duty to do something. Ex: I must study for the exam tomorrow = I have to study for the exam tomorrow = I have an absolute duty to study for the exam tomorrow. On the other hand, "ought" is like "should," meaning that it is preferable that you do something, but you are not under an absolute duty to do it. Ex: I ought to study for the exam, but I think I will go to the movies instead. Note that in colloquial speech, Americans often say "oughta" instead of "ought to." Depending on where you are from in America, you might also say "should" rather than "ought to" more frequently. Finally, "shall" is rarely used in modern American speech except in the expression, "shall we X?" In this case, it is a suggestion, meaning "should we considering doing X?" or "Should we go do X now?" "Shall" has various meanings, including an "emphatic future tense" ("I shall go to school" sounds more emphatic (and old-fashioned) than "I will go to school"), a commandment ("thou shalt not kill" is a commandment given by God that you must not kill), and a suggestion ("shall we go now?") In sum, "must" and "have to" are used daily in the United States. "Ought to" is used as well, but not as much as "should" (at least on the West Coast). "Shall" is rarely used except in set expressions such as "shall we?"

American and English are similar in these cases

"Must" = должен "Shall" = будущее время "Ought" = приходится "Have to" = вынужден