I'm having trouble finding a low cost airline from London to Athens. Any suggestions?

Did you check these:

http://www.whichbudget.com
http://www.skyscanner.net

EasyJet is likely to be the cheapest. However, given the popularity of the route, it still might not be cheap.

Currently Easy Jet has flights from London Gatwick to Athens for as low as 19 pounds. But they are only booking until March right now. You can register online for them to notify you when they add the May flights so you can book quickly and still get a low fare. Easy Jet also flys to Athens from London Luton.

I'm flying into Stansted. How do I get from Stansted to Luton or Gatwick and how long does it take?

Are you flying into Stansted on another budget carrier? I'd put an overnight in between the two flights, because schedule changes are not exactly unknown, and there's recompense if you miss the second flight.

Otherwise, the way to transfer between these airports, or at least one way, is by coach on National Express.
http://www.nationalexpress.com

Some combination of trains and tubes will work too.

WillTravel,
Thanks for the link for National Express. I'm flying from JFK on Maxjet to Stansted.