How can the Ancient Greek deities be defined?

According to G. S. Kirk, the deities of Greek mythology can be broadly divided into two groups: gods and men. Kirk calls the ancient Greek stories about gods "divinity myths" and the stories about men "hero myths." The origins of these fables date so far back into antiquity that their precise beginnings are disputed. It is agreed, however, that some of these tales date well before 1000 B.C. were transmitted orally and used to help man explain the inexplicable (e.g., weather phenomena, the dichotomy of good and evil, the origin of man, etc.).
Kirk divided the divinity myths into three categories: 1) those that dealt with cosmogony and the creation of the universe; 2) the Olympian gods (Zeus, Poseidon, and that familiar cast of characters); and, 3) the stories about the creation of man. These gods were not simply of dualistic good or evil temperaments (angels vs. demons, as it were), but were known for being simply powerful. They had emotions that were usually attributed to humans, such as lust and jealousy. They meddled in human affairs. They fought amongst themselves. These gods were and are dissimilar to the deities (God, Allah) of the Jewish, Christian, and Muslim religions.
Kirk divided the hero myths, too, into three categories: 1) the tales of yore, ye olden sagas that pre-dated the Trojan War made famous by Homer; 2) the more recent tales dating to, and after, The Iliad and The Odyssey; and, 3) the stories about men who were definitely not myths—in other words, men who were historical personages. The men of the first two categories were not "ordinary men in extraordinary situations" as we enjoy reading about today; these were not the typical tales of an underdog, like David who fought against Goliath. These hero myths were about great men doing extraordinary things, like battling the Olympians gods themselves, not merely trifling with a mortal Philistine, so-called "giant." These were not the morality plays of early American history or Victorian England, where the moral of the story was spelled out for the reader at the end ("right makes might," "honesty always prevails," and the like).
Yet, even as both the gods and the men of classical Greek mythology were great, these heroes were also faulty; indeed, most had a fatal flaw that proved to be their undoing. Thus, these sagas served both a cathartic and a pedagogical purpose.