Why were the gods involved in the Trojan war?

Because Eris made trouble at the banquet where she was not invited, and so threw a golden Apple marked TO THE FAIREST. The goddessed all clamored to get the Apple that Zeus finally had to intervene. The choice was finally narrowed down to 3: Hera, Athena and Aphrodite. Paris of Troy judged the 3 goddessed not by their physical attributes but by the gifts they offered him. When Paris chose Aphrodite and handed the Apple to her, the other 2 were enraged and thus sided with the Greeks when Aphrodite sided with the Trojans.