Remember that this passage is supposed to hit home at a personal level and soldiers are (generally) a violent lot. Also at the time (as is still the case in some countries), the soldiers were more than soldiers, they were the main police force. By "Do violence to no man", I believe that John the Baptist was telling them not to abuse their position.

I think that "Don't extort money" fits with no violence since violence is usually needed to extort money.