New cards in the Voice of Isengard like Keys of Orthanc trigger from the doomed keyword. Does this only count player cards or does it also include encounter cards with doomed?

Yes you have the option of triggering Keys of Orthanc from an ally or encounter card that has the "doomed" keyword. The only ally that has the doomed keyword at the moment though is Saruman.

But plenty of event cards have the doomed keyword.

I remember seeing same question some threads before... answer was caleb'ed as doom from encounter is same as doom from player.

When does doom trigger? Can I use Grima's ability to play Keys of Orthanc for free giving it doomed 1 raise ny threat by one and exhaust keys of orthanc to give me one resource?

I believe so, yes, because the Doomed happens after you play the card, so it is in play when you raise your threat and thus you can trigger the response.