MODALS OF OBLIGATION

REMEMBER!

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Must: moral obligation.
Mustn't: (moral) prohibition.
Can: ability, possibility, or permission.
Can't: inability, impossibility, or no permission.
Have to: external obligation.
Don't have to: it's not necessary.
Should / shouldn't: advice or suggestion.

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MUST
http://www.englishgrammarsecrets.com/musthaveto/exercise2.html

MUST, MUSTN'T, CAN
http://www.englishexercises.org/makeagame/viewgame.asp?id=3341#a

MUST/HAVE TO

http://www.tolearnenglish.com/exercises/exercise-english-2/exercise-english-49540.php

http://mbonillo.xavierre.com/exercises/eso4/4eso2007/musthaveto1.htm

HAVE TO/DON'T HAVE TO/MUSTN'T
http://www.eclecticenglish.com/grammar/HaveTo1A.html

http://www.englishgrammarsecrets.com/musthaveto/exercise7.html

Note: sentence 6. The answers provided by the site's self-correction do not make much sense, and all in all the sentence is not a very good example of natural language usage. My advice is  ignore that sentence and continue with the rest.

SHOULD/SHOULDN'T
http://www.englishexercises.org/makeagame/viewgame.asp?id=2865#a

MUST/MUSTN'T/SHOULD/ HAVE TO/DON'T HAVE TO/CAN/CAN'T
http://www.englishexercises.org/makeagame/viewgame.asp?id=3401

Note:
there is a mistake in the first sentence . According to the web site's self-correction, the answer is "shouldn't," but the correct answer is "should."

http://www.tolearnenglish.com/exercises/exercise-english-2/exercise-english-87468.php