Homer's Odyssey ended - according to the latest astronomical calculations - at October 30, -1207 with Ullyses assasinating Penelope's would-be husbands and finding his wife again. Ulyses had help from a supernatural friend of his, a mysterious "man" called "Mentor", which in reality was his patron Goddess Minerva. It was actually the last event of a God's intervention on Earth. A little earlier in an Akkadian tablet of -1960 found in the destroyed Ur, it is written "Our Gods are LEAVING like migrating birds, our cities are in flames.". We also have the claim of the Jews that they took their Ten Commandments from a desert fire deity in -1446.
The strange thing about that last event is that this deity was too much aggressive and demanded exclusive worship. Carefull reading of these ten commandments gives the conclusion this deity does NOT deny the existence of other deities but merely forbids worshiping others than himself. He says "Ουκ έσονται ΣΟΙ θεοί έτεροι πλην εμού." that is "There shall be no gods TO YOU other than me.". That god was very carefull so that he actually tells lies by telling no lie. He led naive people that can't get the difference between "Is not" and "Shall be not to you" to believe that he is the only existing true god. This god like his kind is a very wise and intelligent being that can manipulate a naive human without difficulties...
All these gods appear with great powers but they also had human weaknesses, even the god of the old testament that is SUPPOSED to be all good and perfect, has actually the behavior of a criminal, much worse than the others that SUPPOSED to be imperfect and human-like. So all these gods that ever interacted with humans are human-like and they have much greater power than a human. I don't doubt that mythology exaggerates but their actual power is still much greater than humans.
These gods are immortal and could not be killed even in defeat. Defeated opponents in the world of gods had to be imprisoned for eternity because they can't be killed or else neutralized for ever. I would say that they arent material but energy beings that cast images in our minds so that their "material bodies" with which they appear are just an illusion, an image that they cast in our minds while they exist in their dimension.
It would be a good theory but for one detail that does not match. These gods had kids with humans in both ways: Gods with women and Goddesses with men. So, while this does not utterly oppose our theory they might also have the abity to exist there as well with bodies that are able to interact with our material bodies.
There are two possibilities:
a) Vehicles that fly between the dimensions: They are called Vimana - by the Hindus - or Merkabah - by the Jews - and they had terrible weapons that could destroy cities...
b) A magic Veil, used as a gateway between the dimensions. The veil seems to have something to do with the transition element, the water, especialy in the form of mist along with trees and plants. Rivers and lakes also have something to do with that Veil. This is supported by many myths including elves/faeries and the Arthurian legend.
So these Gods are creatures from another dimension that have indestructable bodies consisting of particles of that dimension that can interact with our world. Modern physics tells us that there is an 11 dimensional universe. In a 6-dimensional subuniverse there can be ten 3D worlds with a common time. That would be the worlds described in the book of Enoch: A chaotic void, a netherworld ("hell" for the christians, Hades for the Greeks), our world and 7 heavens. The first of them is the Faerie Land or Olympus for the Greeks. This is where these human-like Gods live along with faeries, nymphs etc... The Veil lies between this world, the Underworld and the First Heaven. The higher heavens are unknown and completely incomprehensible to us.
I think that none can really know what ended the mythical age leaving only whispers in the wind behind. The Arthurian legend is far more recent than Homer's epics and this gives me hope that what was lost may still be found again.