Historically they are depicted as characters who are capable of dying (though VERY hard to kill) and possessing of immense power.
As to whether or not they are gods, that depends on your definition. They are certainly powerful beings, but their origins are not explored. They are shown with many powers and abilities, many of which aren't shown by any non-'god' characters.
That said, their divinity is at the mercy of the writers. At any point where it's convenient, they will be retconned into powerful aliens. Then back into gods. Then they'll retcon them into being alien gods.
Suffice to say that Wonder Woman thinks they are gods, and the rest of the Justice League, at least, tends to follow her lead (either because they agree or are simply polite/trying not to annoy the powerful magical beings).