I'm trying to sync up a song with lots of strumming on EoF. but the chords seem to snap into place (like at the quarter or eighth note spot). How do I get them to stay in weird positions?

To turn off the grid snap just press G.

 

If you get problems caused by a variable tempo, this topic has some info on how to make a beat map:  http://customsforge.com/topic/5099-how-to-sync-your-beat-map/

You can also just use a higher grid snap setting (like 1/48) if you want.