For Omnitron, if at the end of his turn I pull a repair drone from the trash, does the drone do it's end-of-turn healing, or do I wait for the next round's end of turn?
Thanks for any help!
It does the healing because you are still in the end of turn phase.
…and the same goes for anything that comes out during the End Phase of a turn and has an end-of-turn action - the new card becomes last in the line of cards that might need to be played in that phase, and so gets to do its stuff. This is one reason the Chairman can be so nasty - the Operative brings out an Underboss at the end of the turn, who has an end-of-turn action to bring out a Thug, who usually has an end-of-turn action to do something nasty to you. So if it's the Contract, bringing out a Hired Gun, you are going to be shot at the end of that turn (or the beginning, if Ab'Zero's around and has played Subzero Atmosphere) :P.