Here is the basic difference between the words you asked about. The example sentences do not show the different ways the words can be used as they have several different meanings. Please do not assume that my examples are the only proper way to use the words! "Have to" and "must" both imply that a person has no choice when making a decision. An example, sentence is, 'I have to go to work to make money.' "May" and "can" show that a person has a choice when making a decision. An example sentence is, "I can go to the movies, but I may decide to go to the play instead." "Might" suggests that you are unsure about an action. An example sentence is, "I might eat Thai food for dinner, but I am not sure if I want to make it." I hope these have helped!

This is not just academic English - it is in common use in daily speech. I'm afraid you'll just have to sit down and learn the modals properly. They can be quite flexible in English, and a short explanation will not be enough to help you properly. If this helps, look up "modals of obligation", "modals of permission" and also "modals of deduction". For a start. That may help you organise your thoughts.