As far as I know as a pre-intermediate level speaker: Must - strong advice You must be quiet! Mustn't - prohibition You mustn't smoke have to - assumed obligatory I have to do homework haven't to - not compulsory You don't have to worry about these details Can? - Asking for something softly Can I have another cup of coffee? Could? - Asking for permission Could I ask you something personally? Would? - Offering something Would you like another beer? wouldn't - assumption Wouldn't this be a bad end? might - i'm sure of something This might be the right house. may not - i'm sure of something (not) He may not vote this time. may? - Asking for advice May I study English? should? - Asking for opinion Should I stay or should I go? should or shouldn't - giving advice about yes/not to do something You should call him right now. You shouldn't be here. Maybe I forgot someone, but I think this is a good start.

must/should Must is stronger than Should. "You must drink water to live!" "you should drink more water (but you don't have to)." can/may Can means you have the ABILITY to do something. May means you are ALLOWED to do so something. "I can count to 10 in Italian." "Once I have my passport, I may cross the Italian border." Some speakers use can/may interchangeably Could is conditional/past tense of Can will/might Will is more certain Might is less certain, but still possible "I will call you tomorrow! I promise." "I might not come to work tomorrow. I think I'm getting sick."

Have a look on this lesson, it'll help you :) http://learningwithjohn.com/grammar/modal-verbs/