It should be explained how a Monster can die at the hands of Heracles, Samson, AND a certain famous Space-Jammin' athlete. See, the reason that the gods in the Overworld have any relevance in the Scion universe at all falls to three factors: Belief, Remembrance, and Fate. Belief is what created the gods, and Belief helps sustain them. As long as there are at least a few mortals in the World that venerate the old gods, the gods' existence is assured. Remembrance is the main force that keeps the gods powerful the same way a Scion's Legend keeps them powerful. There may not be many mortals who worship the ancient pantheons, but thanks to fifth grade history curriculums, they won't ever be completely forgotten. Finally, Fate is the only thing capable of making a god feel fear. A god won't ever truly cease to exist until its fate has been fulfilled, as the Aesir have learned and constantly fret about. Even the Dodekatheon, arguably the most powerful pantheon, is afraid that Fate will repeat itself and that their children will rise up and destroy them the way they threw down their own divine parents, the Titans, and the way the Titans threw down their parents before them.
Monsters only need one thing for each and every one of them to be well and truly immortal: mortal FEAR. As long as mortals fear the dark, the unknown, death, public speaking, what have you, no monster will ever truly die, no matter how many times a Scion cuts its head off or incinerates it with a burst of concentrated sunlight. Such an attack will certainly destroy a monster, and send it back to the Underworld that spawned it. However, depending on how thoroughly the monster in question was killed, how powerful the Hero was that killed it, or how powerful the monster itself is, that monster's essence will collect in the Underworld and break free to terrorize the World once again, which explains how Heracles killed the same Nemean Lion that Samson and Michael Jordan killed. In fact, certain powerful Monsters of legend have the capacity to learn and grow and adapt to the changing world even as the fears of mortals change and evolve to include things that mortals didn't even know to be afraid of. But that doesn't mean that killing Monsters isn't worth it (as they're just going to come back, anyway.) After all, Monsters leave behind powerful Trophies, and depending on the monster and how thoroughly (or how powerful) the Scion killed it, it could take a long time, even centuries, before a Monster is able to collect itself and emerge from the Underworld. But sometimes, a Scion's Fate is tied to that of a particular monster, which will lead to the ultimate demise of a demigodly Hero, the once-and-for-all destruction or dispersal of a particular monster, or (in the case of the Aesir) both.
Also, Monsters turn into dust and ash once a Scion or god kills them, which saves Heroes a good deal of explaining and terrible cleanup.