Ok so any card with a "end of turn" effect drawn from Omnitrons "draw at end of turn effect" takes place?
So end of turn draw a card off the top of the deck, it's the healing bot so Omnitron gets healed?
Just so. You have it.
Continue performing end of turn actions, in the order the cards entered play, until there are no more end of turn actions in play. Same for beginning of turn actions.