Couple of things to add. The Edge used (and probably still does) not one, but two TC Electronics 2290 rack digital delays. While you can cover his style really well with just a single modern delay (TC Electronics actually sells their delay unit in pedal form now), there are a few cases where he's likely feeding one delay into the other to setup up multiple rhythms. Modern delay units have "multi-tap" settings, but they can be tricky to emulate the sound of a setup where one independent delay is being fed into another. Eventide has produced a very flexible delay pedal called the "Timefactor" that is actually two independent delay pedals in one. This not only allows for cool Edge like effects, but also allows you to do some David Gilmour stuff where he sets up a delay pedal for infinite repeat, feeds it one chord, then cuts off the input and uses the other delay to play over top.
If you do a Youtube search for the Timefactor, there are some pretty good, clear demos on how people are using the pedals to get the sounds you're looking for. Also, search for "How to play U2 Bad" or "How to play U2 Where the Streets Have No Name"... you'll get a fair number of choices, but in there will be some videos that explain exactly how to play those two songs, including how to setup the delay. They are both vintage Edge tunes, and pretty easy to play.
As a jumping off point for your own playing, you might want to check into the Adrenalin III pedal... it has a number of tempo driven effects on it that allow you to come up with some pretty cool sounds. Again, YouTube has a bunch of videos on this pedal.
