When you say “onset”, it makes me think of the onset of a disease or condition or some other thing that you don’t really want.  (The OED says “The beginning of some (esp. unpleasant) situation, condition, or state”.)  Examples that I have found on the internet include “onset of winter”, “onset of a cold”, “onset of puberty”. The “outset” is more like the beginning of an event, like you’re setting out on an adventure.  (The OED says “The action or fact of setting out upon a journey, course of action, business, etc.”.)  This word is most commonly used in the phrase “from the outset” – for example, “I knew from the outset that this was a bad idea” (where “from” means “since”, not “beacause of”). I’m not sure about “offset”.  A more common use of the word “offset” is to refer to a physical or numerical distance (the OED says “linear or angular displacement; the amount or distance by which something is out of line”) – for example, if I were setting up some rows of chairs, I would want the second row to have a slight offset from the first, so that the people in the second row could see.  If trying to group “offset” with “onset” and “outset”, I think it means pretty much the same as “outset”.