In a bit of a Sticky Wicket

Also remember that while the god will want the item(s) back; so will that god's enemies or rivals.

You could pretend that the higher powers are only vaguely aware of where the item is and they send in some low level cultists in to do the leg-work of finding the item.
If the PCs aren't aware of the power they hold in their hands, then the interest of the cultists could be quite a mystery to the PCs

If it's too late for that, if they aren't aware how to activate the power in their hands; it could lead to quests to find activation words, etc. But activating more powers might make the item more visible to both sides and bring in bigger threats to the PCs

Garl's axe is kind of an odd thing. Garl is normally thought of as an inventive/trickster deity, not a straight-ahead warrior, but a battle axe is really only good for chopping at things. It's not a sly, subtle weapon of the sort that one would expect a god who specializes in illusion to wield.

There's a variant myth in one of the Greyhawk sourcebooks (I think Ivid the Undying) in which it is Garl, rather than Corellon Larethian, who faces off against Gruumsh in single combat and perhaps even cuts out his eye. So there's support for the idea that in very early myths, Garl was more of a war god carving out a place for his people with bloody force rather than amusing pranks. Maybe Garl disguised himself as Corellon in order to deflect blame from himself and his people.

But I think it might be fun if Arumdina better fit Garl's personality. Perhaps she seems to be a simple battle axe at first, but she's actually something like a magical Swiss army knife, able to manifest any tool the situation requires, transforming into a hat or umbrella or toothpick or spatula or screwdriver. Perhaps the whole axe shape is mostly illusory. The PC might not discover until much later that she only creates illusory wounds, and all the enemies the PC believes were dead were only tricked into believing they were dead. When they realize they aren't dead at all, perhaps weeks later, they might be furious.

For the Spear, as Athena was a goddess of wisdom (I think that would translate to INT in DnD) and of (strategic) warfare; there might be some ideas for tests or rivals there.

For example, perhaps Ares/Mars wants the Spear (either to keep or destroy) so that he can solidify his portfolio of warfare. Since he isn't flat out evil and since the Greek gods seem to be required by the Fates to let mortals with superpowers (or super-magic items) work out their own destinies; he might be able to send challenges but not be able to intervene directly and take the Spear.

Perhaps the Spear, or Athena's agents, will provide puzzles or guide the PCs to puzzle-type dungeons that the PCs must solve (without the help from the Spear) in order to activate a new power of the artifact.
[Imagine the spear pulling like a compass needle or a divining rod to get PCs to the site of the puzzle]

Perhaps Ares and Athena will agree to a "contest" for their respective champions. The contest would have to be one that Ares feels his champion will win with brute force and be one that Athena feels that the PCs can solve if they are clever.
[I know that still leaves the big question of "What kind of contest would accomplish that?" but I don't have any suggestions at the moment]

[My apologies to VanWormer as I somehow overlooked that he had already come up with the Ares/Athena rivalry (until I read Surreal Personae's recap below). I didn't mean to steal or to tell a watered down version of what had been told before]