If the spell targets a creature, it can target a creature-fied god, such as Athreos. If the spell's effect would do anything to it, it does that, wether that thing would cause Athreos to stop being a creature or not.
If the spell becomes a permanent that requires Athreos to be a creature (such as an aura with Enchant Creature), and Athreos is no longer a creature, that permanent stops effecting Athreos.
If a spell causes a physical effect to the Athreos card (tap target creature; target creature gets a -1/-1 counter, etc), and Athreos stops being a creature after the spell resolves, those physical changes remain (he stays tapped until his controller's next untap, he keeps the -1/-1 counter, etc).
Finally, the card "Athreos, God of Passage" is a creature card in every zone except the battlefield. This is because the word "creature" is printed on the card, so it counts as a creature in the hand, library, exile, graveyard, on the stack, in the command zone, and anywhere else I may have forgotten to mention (I dunno where that might be).
Anyway, more than you could ever want to know about Athreos, from your friendly local judge.>>33597266
I like Spectra Ward to go with Heliod's Pilgrim. Makes for a good target lategame, and turns your Archer into a nice finisher.