NPR and AP go with "Gadhafi." We figured it was just arbitrary, but no. There's a source. Back in 1986, Jill Swanson's second-grade class wrote letters to Gadhafi, and much to their surprise ...
Jill: We received letters back from Gadhafi. And his name is spelled in English. That's where we learned we would spell his name G-A-D-H-A-F-I.
Ian: So this letter was, sort of, an English spelling right from the source.
Mike: It's like the Rosetta Stone of Gadhafi.
Jill: Yeah, I guess so.
It's not like Gadhafi goes around writing down his name in English a lot, so that's where NPR and AP get their spelling: from a letter Moammar Gadhafi wrote to a bunch of second-graders in Minnesota. By the way, he also thanked the students for condemning the barbaric actions of the United States, which they insist they did not.