Old English god "supreme being, deity; the Christian God; image of a god; godlike person," from Proto-Germanic *guthan (cf. Old Saxon, Old Frisian, Dutch god, Old High German got, German Gott, Old Norse guð, Gothic guþ), from PIE *ghut- "that which is invoked" (cf. Old Church Slavonic zovo "to call," Sanskrit huta- "invoked," an epithet of Indra), from root *gheu(e)- "to call, invoke."
But some trace it to PIE *ghu-to- "poured," from root *gheu- "to pour, pour a libation" (source of Greek khein "to pour," also in the phrase khute gaia "poured earth," referring to a burial mound; see found (v.2)). "Given the Greek facts, the Germanic form may have referred in the first instance to the spirit immanent in a burial mound" [Watkins]. Cf. also Zeus.
Not related to good. Originally a neuter noun in Germanic, the gender shifted to masculine after the coming of Christianity. Old English god probably was closer in sense to Latin numen. A better word to translate deus might have been Proto-Germanic *ansuz, but this was used only of the highest deities in the Germanic religion, and not of foreign gods, and it was never used of the Christian God. It survives in English mainly in the personal names beginning in Os-.
God bless you after someone sneezes is credited to St. Gregory the Great, but the pagan Romans (Absit omen) and Greeks had similar customs.