1) "breach" usually refers to a barrier of some sort, such as a wall. e.g. "Sir, the wall has been breached by the enemy. Should we fall back now??"
2) "break" is the most commonly used of the above four words, and can be used in almost any context
3) "violate" usually refers to a law or right, such as "that country violates it's peoples' human rights" or a person's integrity ("violate" in that context is often synonymous with rape")
4) "defy" usually refers to a regime, or some kind of other person or institution, it usually infers willful action against another person's wishes