I'm not clever with quoting mechanisms -- to get things done without great consuming of time, I'll "brutalise" things a bit.
Willy Nilly wrote: "The 'g' sound in gyro would be closer to the 'j' in joke, or the 'g' in general (which to me both start with the exact same sound, if different letters), not like 'g' in good. So gyro, gyrate, general, joke, gender, justice, gentle, gee [whiz] etc all start with the same sound."
Right, WN, "I get you". In this instance, UK and US English are on the same page pronunciation-wise.
My original point was (to the poster who seemed to think guy-ro was horribly wrong), I think they are all correct.
The thing about foreign words adapted into English is there are a lot of pronunciation factors at play. The regional pronunciation on the Greek person, and the regional pronunciations of the English speaker picking it up, etc.
I tend to think geye-ro is the most linguistically comfortable because of gyro-scope and gyrate, both which are the same root word, which is to turn, as gyro meat is on a pole that turns, one side always at the heat, one side exposed to allow it to be cut.
Response here, is on culinary / national, rather than pronunciational, lines -- but I find this stuff interesting. In the UK, there are rather few Greek "eateries", but very many Turkish ones (this, I gather, because of ramifications of the Cyprus issue). Essentially, though, often much the same kind of stuff, made by two frequently bitterly-at-odds nations. Greek "gyro" -- meat on a turning pole -- is Turkish (the very same thing) "doner". Most Brits are familiar with "doner" and "doner kebab", but would be at a loss if offered "gyro".