Socrates certainly did not believe in the Homeric gods. In the Republic (according to Plato) Socrates cites a variety of improbabilities and impossibilities about the truth of the traditional Greek myths about the gods describing the inconsistencies and the patent defects inherent in the Homeric notion of the gods. read more
So now on to the question of whether Socrates believed in one God or many Gods. The generally accepted answer is that Socrates believed in an ambiguous monotheistic God. This view is similar to (and I hope I do not offend anyone by giving a simplistic view of) the Brahman in Hinduism. read more
Wikipedia also notes Socrates' unique views on the divine. Socrates' detractors accused him of blasphemy against the gods of the city. Although Socrates paid homage to the gods, he held an ambiguous monotheistic view of an omnipotent, benevolent and just God. read more