Bono himself has said in interviews that he tend to pick up accents. And, of course, it matters to him that the person(s) he's talking to actually understand what he's saying. As have already been mentioned, you can hear a distinct Dublin accent from him in earlier interviews.
Edge's parents may be Welsh, but when he was born, they lived in East London, and the family moved to Malahide in Ireland when Edge was just 1 year old. While not as broad as Larry's brogue, you can definitely tell Edge's got an Irish accent. Just check out the clip of the Dalton Brothers playing 'Lost Highway' in LA - Edge tries to speak in an American accent and he just can't do it. *G*
Adam lived in Oxfordshire, England, until he was 5 years old, but I'd say his accent is probably more of an "Irish boarding school" one. Someone said he and Paul McG talks rather alike, and Paul too went to boarding school in Ireland.
Larry, of course, has got the broadest Northern-Dubliner accent of them all. I've got a friend who's also from Artane, and there are certain words and expressions they pronounce exactly in the same way.
For all four of them, you can definitely tell when they're in Ireland, talking to Irish journalists or addressing an Irish audience: that's when their accents are most audible (perhaps with the exception of Adam).