The Greek /a/ is much closer to the way one pronounces /u/ in "cut".
As for the gamma ("γ"), don't know how to explain its pronunciation as it's a sound that doesn't appear in English... Well, in this case (γ+υ) it's somewhat close to the /y/ in "you" but trying to stick your tongue to the palate (see here for more information and a sound sample). I won't mention how it's pronounced in other cases. (unless you're interested, of course).
Oh... and I have a question of my own: how would one form the aorist of ξανάρχομαι (ξανα- + έρχομαι): ξαναήρθα? It's another possible way of saying welcome back: καλώς <"short subjunctive" of ξανάρχομαι>.