When I encounter a non-English word in Roman Script I tend to default to using the kind of pronunciation we use for Romanized Japanese and Classical Latin (not to be confused with Ecclesiastical Latin).
Ge = "Geh," since there is no "soft" G in Classical Latin or Romanized Japanese (heck, the Romans didn't even have a "J," they just used "i" as a Consonant, making a "y-" sound in front of other vowels).
Note well that the Roman letters used to spell "Julius Caesar" are actually correctly pronounced - "Yoo-lee-us-Kigh-Sar" and written IULIUSCAESAR. You don't pronounce Cicero or Virgil as "Sissero" or "Verjil" either.
At any rate, what does this have to do with Genasi?
Romanization. When you romanize a word that comes from a language that doesn't use Roman Characters (like Japanese), you shouldn't use "soft G" or "soft C" when you find the sounds of a "J" or "S." You are just aping the sounds of the native language into your own script, so you use the "pure" script rather than the exceptions.
Ergo, when I see a purely fabricated word in a fantasy setting I automatically assume it has been Romanized from whatever make-believe fantasy language it came from - and therefore there is no "Soft G" or "Soft C" to be had.
"Genasi" as a Romanization from another language would most likely be "Geh-Nah-See." "Genasi" as a mutated derivative of "Genie," however, would be completely different. Considering the Genasi-Genie-Djinn thing is muddled and tenuous at best in 4th Edition I'm just going with "Geh-Nah-See" until I see a definative pronunciation guide.
- Marty Lund