You're wondering about why the Greek gods are accepted by both sides in Homer's Illiad. Remember that this is an epic poem, and not necessarily an accurate record of actual history. read more
This was the cultural hearth of Greek mythology, so Troy was well within the sphere of influence of the Greek gods. Remember, the people of Ancient Greece believed that places as far as Colchis also worshiped the Greek gods. read more
Most of the names of the Trojans are not Greek and can be found among these other Anatolian languages pointing to a relationship. Of course, in the Iliad Greeks and Trojans speak to eachother and have the same gods. The Greeks certainly had a long tradition of drawing parallels between Greek and foreign gods and giving Greek names to foreign deities. read more