The most likely place I'll hear "set about" is on the topic of fighting. If a man or dog sets about someone, it means they are coming at them, about to deal with them. Similar to "tackle" which also has a fighting meaning as much as a non-fighting task-oriented meaning. When setting about someone or something, you're literally setting yourself on a course concerned with / dealing with them.
The main place I'll hear "set off" is when someone is leaving, to begin a journey, they will "set off" when they are going on their way, beginning their journey. Literally, they are getting off of their current spot, and moving towards their destination.
As for "set down to", I don't recall ever hearing this before. But "get down to" is quite common and has a similar meaning to those discussed above.