@Hogan, I never saw his Streetcar or his More Stately Mansions, so I can't speak to those specifically. However, I have seen 11 of his productions - the oldest of which was Roman Tragedies. I've said this many times before, but I believe that Ivo does his best work when he's directing material written originally for the stage, as opposed to the film/book adaptations that he's been doing more recently.
As for what, specifically, his "bag of tricks" consists of, here are a few that come to mind:
--mostly-barren stage, particularly with a lot of whites, grays, and off-whites.
--often a subdued, slightly sluggish pacing to his scene-work.
--making messes onstage
--live-feed camera work throughout the show, especially following actors backstage, and even outside the theatre.
This last one (camera work) is interesting, because it's arguable his most "innovative" trick, and we've seen it used quite a lot more frequently in recent years, especially in Europe and the UK (including by Robert Icke - mentioned above). And yet, he uses it so much, that it's also become his most stale schtick. Although I actually did like the way he used it in West Side Story - but again, that goes back to my first statement about his work on adaptations vs. revivals.
RE Robert Icke: I absolutely love his work - his Hamlet remains one of the best pieces of theatre I've ever seen. But again, I think a lot of his "innovations" really come from his colleagues and predecessors. The most unique thing I've ever seen Icke do was in "The Red Barn" at the National, where he used sliding black scrims to create tight "frames" onstage, resembling camera frames, without using any cameras.