in short: what are some good methods for turning a mic-recorded or synthesized sound into a more "old-school", even 1930's sound? Thanks!

Well it may not be the answer you're looking for but you could do a lot worse than check out Izotope's free vinylizer plug: http://www.izotope.com/products/audio/vinyl/
 
It has various controls for adding vinyl noise to a track - warp, dust, scratches, electrical hum etc. But what might interest you more is the "year" dial with which you can select decades from the 30's to the present day. I find it to be one of the most authentic "oldifiers" out there. Even if you're not specifically looking to age your track, it's also great for creative tone shaping. Try putting a Rhodes keyboard part through it set to "60's" - magic! 
 
Be aware that there are both Direct-X and VST forms of the plug, and the "warp model" selector only works with the Direct-X version. 

The only synthesizers around in the 1930's were the Theremin and the Hammond organ.
 
If you mean band-limited, to emulate the limited frequency response of 78-rpm records, that's just EQ and maybe a little distortion.
 
SDDR seems well-suited for that kind of thing. At least, their audio demos seem to make everything sound like it was recorded - badly - in 1932.

T-Racks 3 Deluxe has a number of mastering pre-sets that can give the final mix a 1930s feel to it.

If you want your sounds more old school as in use by bands like Boards of Canada. Then I would consider popping some chorus and saturation on the synth, coupled with good eq'ing and maybe a little lfo/pitch modulation.