In terms of The Odyssey by Homer the limits the gods possess seems to be through another god.  While they are able to exercise power of the world of the mortals, their own limitations would be at the hands of another immortal.  For example, Poseidon has nothing but disdain and anger for Odysseus in the manner in which the hero treated his son and his overall demeanor.  Yet, while Poseidon does have his way in causing challenge in Odysseus predicament, his full desires are thwarted by Athena who constantly favors the mortal and seems to always provide a bailout to him while in trouble and despair.  The polytheistic composition of Greek divinity establishes an understanding that the desires of one God or Goddess can be maximized and fulfilled, but is always limited through the presence and power of another immortal.

What limits do the gods have in The Odyssey?

In a way, you can think of the gods as beings more like super heros than like gods.  They can influence people and some events, usually according to their various areas on influence, Poseidon on the sea, for example.  But they often cannot force people to do certain things, they have to try and influence people by using their own tendencies or desires against them.  Because of this, they often work through other humans, or other beings, because they cannot simply force someone to do exactly what they want.  They are also often limited because of the actions of other gods, if they don't have the approval of everyone, they can be limited by the actions of another god.