Because keeping all of those quotes, notes, and rumors in one post is getting lengthy, let's break this down by team in separate posts. As these come in, they will be updated and reposted.
Henry Schulman (and here, and here) (5/21):
Doubt Oswalt will be moved soon despite trade request. Astros will want bidding. Anyway, Gs don't need Oswalt, but a bat. (In the two tweets following, he notes that Berkman makes more sense, and the Astros wouldn't need Madison Bumgarner or Buster Posey to get the job done. Like we need Buster Posey, with Castro in Round Rock.)