I don't think Hilgya's plan can work at all. If it could, there would be other high-level characters from previous worlds (or their descendants) hanging around in the outer planes or even planeshifting back to Stick world. Come to think of it, that could explain how Fruit Pie the sorcerer ended up in Dorukan's fortress, but it raises way more questions that it answers. It seems safer to assume the gods have some sort of contingency measure in place.

On a more general level, my personal take about leftover oathspirits is that blood oaths or similar rituals are about killing a foe (or destroying them, for pedantic wizards). At least, that's what the standard tattoo procedure shown in Start of Darkness seems to suggest. The only other example that we have is Violet, whose descendant had to sunder a cursed sword.

As Roy points out, if the world ends in a way or another, all blood oaths are technically fulfilled. Therefore, any remaining oathspirits would be allowed into the afterlife. Probably Mechanus for Eugene, as he doesn't strike me as "good", plus I think filling paperwork until he's bored out of his immortal mind would be pretty fitting.

I do wonder whether he really is the last oathspirit or not. Maybe the devas were so pissed at Eugene that they separated him from the others without telling him (it's not like there are any landmarks to help him find his bearings in this demiplane). He did bind and gag Tony, after all.

On a semi-related note, I never noticed Roy's plan with his archon was still pending.