On the Dodgers: last time was about 1980, vs Yankees. MVP? I can't remember, although the Yankees had three lefties starting: Guidry, John, and [somebody I'm forgetting]
That was the last time the Yankees went to post-season until about 1994 or '95...the year they lost to the then-intact Mariners. Yankees promptly got Tino Martinez from Seattle to play 1B, and won about 5 of 6 WS.