I ask this there since I would think the Greek gods would be the most involved thanks to Wonder Woman and have the most examples.
Whenever I try and get even a vague idea of what the gods in the DC are capable of and what limits they have I find it practically impossible. One story will state they depend heavily on mortal worship and another has them perform feats like it does not depend on it. Some stories have them being able to do practically anything and others they are much more vulnerable. Is there even a vague idea of what their limits are or has it traditionally been up to the story and whatever the writer wants?
Do they more or less follow the traditional rule that the more aloof and distant a god or cosmic being the more mysterious and powerful they are capable of doing just about anything, but the moment they begin to widely interact with the larger universe or Earth's heroes they become in a sense much weaker and vulnerable to mortals with their powers becoming much more limited?