"Might" is both the past tense and quasi-subjunctive of "may" and is used when it applies to (a) an event in the past or (b) alternatively a tentative or unlikely situation in the present. Examples:
a) "The judge says I may go" becomes in the past "The judge said I might go".
b) "I may catch the bus tomorrow" vs. "I might be run over by a bus tomorrow".
The main difference between "must" and "have to" is that the latter is not a modal verb, so it can form all the usual verb tenses and compounds, such "I will have to to move when I get my new job", or "I didn't have to move". When you could use both, I think there tends to be a slight tendency to use "must" when it's intrinsically true, versus something that's externally imposed and perhaps could be avoided. I might say "I must go to the dentist, because I have this toothache that won't go away" but "I have to go to the dentist for my teeth-cleaning tomorrow".