All three words seem to have similar meanings, but I am assuming the difference is that each may be more appropriate in different contexts. I am particularly interested in their use when talking about evidence, principles, or in the context of an argument, like:
"Contradictory evidence", "Contravening arguments", or "Controverting a position."
Here are the definitions I found (which may explain why I am confused about appropriate usage):
1. to go or act contrary to : violate "contravene a law"
2. to oppose in argument : contradict "contravene a proposition"
1. to assert the contrary of : take issue with "contradict a rumor"
2. to imply the opposite or a denial of "your actions contradict your words"
1. to dispute or oppose by reasoning "controvert a point in a discussion"