Modal Verb: Have To

"Have to" is used to express certainty, necessity, and obligation.
Examples:
- This answer has to be correct. certainty
- The soup has to be stirred continuously to prevent burning. necessity
- They have to leave early. obligation

http://www.englishpage.com/modals/haveto.html

Modal Verb: Might

"Might" is most commonly used to express possibility. It is also often used in conditional sentences. English speakers can also use "might" to make suggestions or requests, although this is less common in American English.
Examples:
- Your purse might be in the living room. possibility
- If I didn't have to work, I might go with you. conditional
- You might visit the botanical gardens during your visit. suggestion
- Might I borrow your pen? request

http://www.englishpage.com/modals/might.html

Natural Lives

Modal Verb: May

"May" is most commonly used to express possibility. It can also be used to give or request permission, although this usage is becoming less common.

Examples:

- Cheryl may be at home, or perhaps at work. possibility
- Johnny, you may leave the table when you have finished your dinner. give permission
- May I use your bathroom? request permission

Modal Verb: Must

"Must" is most commonly used to express certainty. It can also be used to express necessity or strong recommendation, although native speakers prefer the more flexible form "have to." "Must not" can be used to prohibit actions, but this sounds very severe; speakers prefer to use softer modal verbs such as "should not" or "ought not" to dissuade rather than prohibit.
Examples:
- This must be the right address! certainty
- Students must pass an entrance examination to study at this school. necessity
- You must take some medicine for that cough. strong recommendation
- Jenny, you must not play in the street! prohibition

http://www.englishpage.com/modals/must.html