"I did BADLY IN my exam" is the only correct sentence. If you write "I did bad..." it means you did something that was malicious. (Plus, "I did bad..." sounds clumsy.) Use "on my exam" to mean something written on the exam paper, eg. the questions, or even your final mark.

I did bad on my exam(s) For the opposite you can say: I did well on my exam

Your best choice is: I did not do well on my exam or I did poorly on the exam I thad taken.

the last one because you are trying to emphasize the verb, so it has to be followed by an adverb (badly) and the correct preposition is "on" (but that is just a fixed rule I guess)

I dont know how well I learnt my English but I always said, in exam. I did bad in my exam/exams. check the question asked here http://uk.answers.yahoo.com/question/index?qid=20110115055851AAmTnfq