Break down is generally used for cars (my car broke down - it didn't work) and for mental state (she had a breakdown). It can also be used for definitions and sharing information (will you break this down for me so that I can understand).
Break out is used for acne or other skin conditions (he broke out in a rash) and for someone gaining a lead or doing something well (it was a break out hit).
Break up is when you end a relationship with a boyfriend, girlfriend, partner, etc.
Break on...I'm not familiar with that.
And, there are likely others that I can't think of, but those three above are quite commonly used.