John Michael Greer, who is himself a polytheist, somewhere notes that most arguments used by atheists don't make any sense against polytheists; and it doesn't take much to show this to be true. I was put in mind of this today by someone talking about how, to an atheist, 'God', like 'Zeus', does not refer to anything that exists.
The problem, of course, is that polytheists can usually point to their gods, at least some of them. We see this with the dialogue Epinomis. If you asked Philip of Opus, assuming that he was the author, whether the god Ouranos existed, all Philip would have to do is take you outside and point up at the sky. And he could also point out Zeus to you, without any trouble whatsoever; later Roman polytheists, of course, following along, would point to the same exact, obviously existing, thing, and tell you that it was Jupiter. The entire reason we call it Jupiter is because some polytheists pointed it out as their god, Jupiter. 'Zeus' refers to something that exists; someone who disbelieves in Zeus just thinks that the existing thing is not, in fact, a god.
In general, the rule with polytheists is that they cannot be refuted by arguing that their gods simply don't exist; as I said, they can usually point to at least some of their gods. The only way a polytheist can generally be refuted is to argue that what he is pointing to in the world is not actually divine; arguing that it doesn't exist is not a viable way to go. Long ago, in reading something or other on (I think) scientific reduction, I came across a passage in which the author repeatedly used the example of Thor's Hammer: Once lightning was thought to be Thor's Hammer, and now it is known that it is electrical discharge. It was, of course, just a stand-in example, rather than any serious comment about Mjölnir. But if you were to ask any actual Asatruar, he will point out that in Ásatrú, there is no denial of the electric discharge description when one uses the Mjölnir description; the point was never that lightning was an ordinary warhammer, which any ancient Viking could easily have already told you it wasn't, but that it was Mjölnir, i.e., lightning, which is Thor's, and it is called a warhammer because it can do what a warhammer or battle-ax does on a scale suitable for a god. And no matter how thoroughly atheistic your theory of electricity is, I can without any hesitation guarantee that it has not established the nonexistence of lightning.
This is, interestingly enough, a feature that polytheists share with pantheists; it is even more obviously impossible to argue that what the pantheist calls 'God' does not exist, because you have only to look around to see that it does. The only question is whether it is, as they say, divine.