This probably needs some unpacking, while also offering some historic clarification.
In the 2nd Temple period of Judaism there developed the idea that the false gods of the nations were "demons", evil spirits. We can see a bit of this, for example, in the word Belial, which is a corruption of the various ba'als of Semitic paganism from the Levant, such as the Akkadian Ba'al Hadad, or the Phoenician Ba'al Hammon. Where Belial had become an alternative name for Satan. While post-2nd Temple Judaism, under the Rabbinate ceased to believe in the idea of fallen angels, and of a devil figure, the idea was obviously preserved in Christianity.
St. Paul addressing the Christian community in Corinth--largely comprised of converted former-pagan Greeks--the Apostle focuses a lot of attention on speaking against Christians returning back to pagan practices. So in his first epistle to them, 1 Corinthians, in the 10th chapter he makes a contrast between the Christian celebration of the Eucharist and pagan temple ritual meals. In making this argument he says that one cannot eat at the table of the Lord and also eat at the table of demons. The implication being that participating in such pagan rites honored demons.
And the Church, rather consistently through history, would argue that those who worship false gods are giving honor to mere demons, not to gods.
Now, this is where some clarification is probably important. It's not that, for example, when someone said a prayer to Zeus that there was a real being called "Zeus" and that this being was a demon. Rather, because the demons are liars and misfits, they want men to worship false gods rather than the true God. Thus idolatry is a lie, it turns men away from the Creator and to things which are false and are not real. It is this falseness, this lie, this spiritual delusion that is attributed to the demons.
We can actually see this in another part of the Canon Episcopi which I quoted above,
"It is also not to be omitted that some unconstrained women, perverted by Satan, seduced by illusions and phantasms of demons, believe and openly profess that, in the dead of night, they ride upon certain beasts with the pagan goddess Diana, with a countless horde of women, and in the silence of the dead of the night to fly over vast tracts of country, and to obey her commands as their mistress, and to be summoned to her service on other nights."
However, the Canon is clear in its position--this isn't actually happening, it is nothing more than the mind being deluded,
"Wherefore the priests throughout their churches should preach with all insistence to the people that they may know this to be in every way false, and that such phantasms are sent by the devil who deludes them in dreams. Thus Satan himself, who transforms himself into an angel of light, when he has captured the mind of a miserable woman and has subjected her to himself by infidelity and incredulity, immediately changes himself into the likeness of different personages and deluding the mind which he holds captive and exhibiting things, both joyful and sorrowful, and persons, both known and unknown, and leads her faithless mind through devious ways. And while the spirit alone endures this, she thinks these things happen not in the spirit but in the body. Who is there that is not led out of himself in dreams and nocturnal visions, and sees much sleeping that he had never seen waking? Who is so stupid and foolish as to think that all these things that are done in the spirit are done in the body,"
In other words, spiritual delusion--not actual manifest power of any kind--is the work of the devils; the gods of the nations are not real, and they have no power; but the devil is a liar and so it is delusion which leads men away from the truth of the one God through superstition.
That's the historic Christian position.
Not that the Egyptian Osirus or Anubis or Ra et al are real, but they are false--they don't exist. And the worship of these is false spirituality, false religion; the devil's role is through trickery, lies, and deceit. Not that he has himself god-like powers.
Having said this, I have met a number of Christians who have tried to argue that the gods of various pantheons are, actually real, and that each one corresponds to an actual demon, and that said demons have actual, real power. But this seems to be a very modern heresy.
-CryptoLutheran