If my memory serves me right, I can play Anodyne and a bunch of other flash/AIR-based games on Windows with an overlay. Now, I'm on OS X and I can't seem to pinpoint any valid solutions. Is there a "hack" or a way to make it work on OS X?
Steam distributes different versions of the game you're playing depending on what system you are on. As developer Edmund McMillen has said about his game The Binding of Isaac (another flash based game) earlier, it takes quite a bit of fixing from the developer's side in order to make the Steam overlay (and, in some cases, achievements) work in flash games on OSX.
Unless Seagaia (developer of Anodyne) and the other developers of the games you are referring to decide to properly implement/fix the Steam overlay for OSX, the overlay will not work on OSX.