Royan, thanks for the info, but they're definitely not strobes--they're the landing lights (the big headlight-ish sorta things).
The corporate aircraft theory probably most closely matches what I saw. The last aircraft I saw flashing appeared to be something Lear-sized, I think. It's possible that one of the other times may have been a 737, but I didn't get a close enough look to tell. (Oh, and SWA doesn't fly into DCA...at least, I've never been able to get a flight outta DCA on SWA -- always BWI).
Anyway, thanks to all for the info!