What are the defining traits of a god?

My game setting is loosely based on pre Columbian peoples of Central America and the Caribbean. There is a lot based on Taino and Carib mythology as well as the Aztecs and their predecessors. A lot of the religions have been based on real world counterparts with my own twists on them. Like combining Roman imperial cults with the idea of the Mesoamerican tonali, or hero cults and expanding on the Hero Twins motif we see. In particular, I was really fascinated with astrology and numerology and its place in the Mesoamerican religions. And there's other inspirations in there for more pagan, syncretic beliefs, like Vodou and Santaria, or more monotheistic religions, which in this setting comes from the colonists and is inspired a lot by Gnosticism. 

But yeah, lots of inspiration from the Tainos, Aztecs, and Mayans. Zemis in particular are nature spirits from the Tainos of the Caribbean that live amongst the rainforests on the islands. I need to pick up the ACKs Player's Guide so I can run Shamans in my game, since they'd really make more sense in the setting :)