As in most languages, God figures in a lot of expressions and exclamations, and English is no exception. However, care must be taken with this word so as to not offend anyone. In this usage, both God and Man are used to emphasize your impression of something — usually right when you're experiencing it. Here, it has a nuance of I JUST HAVE TO SAY (HOW (MUCH))... For instance, in the snippet below, as soon as the cake hits the speaker's taste buds, he realizes HOW delicious it is and can't hold his tongue. 

However, this can also refer to something negative. When followed by a verb form, such as irritates in the following example, it expresses HOW MUCH you feel it; to what extent it affects you. Say your sister has a habit of talking in a whiny voice whenever she asks your dad for something. You hear her do this and can't hold your tongue... you say God, she irritates me when she talks like that! to express HOW irritating it is to you. By the same token, you could say things like God, I'd kill for a beer right now! -or- Man, I hated that movie!

Here, intonation is everything. God/Man is pronounced at a high pitch, depending on  your level of excitement, and the next word follows immediately at your lowest pitch, and the rest of the statement stays on that low pitch... no matter how long it is! For example, God/Man, she irritates me when she talks like that! Note that there's no pause between God and she.

Also note that Man as an exclamation has nothing to do with the gender of the person you're speaking to. It can be used with women and children because you're not using it to address them directly.