Well, I'd say it doesn't really matter as the proper spelling is Gödel; oe is just used by people who for some reason can't use ö. (And some people, me included, do prefer using o for ö when neccessary. It looks more like the original, and those who know the words can usually figure it out anyway. There are exceptions though - in Norwegian "høre" means to hear, but "hore" means whore. Oops! Did you whore what I just said?)
On another note ♪ I noticed we've only been using the short version of the title of EGB, so I thought I'd try to get something out of "An eternal golden braid". On the first try the trusty anagram generator tossed out a bunch of lines starting with two or three single A's. When I set the minimum word length to 2 it came up with 75 001
anagrams including BANDANA ENROLLED TIGER and TELLER IGNORED BANDANA. Try to come up with a plot for that! 
