It's the last war on Earth, men and women are the last opposing armies, and when they've killed each other, humankind will end. The girl Lilly, a virgin, not yet a woman, not yet a combatant tries to escape the carnage. She's looks human, but she really isn't quite, she has such fine senses that she hears plants cry out in pain. For a time she escapes the war, and lives outside of reality.
She sees a rough and tumble unicorn, and makes her way to a ramshackle farmhouse. She finds an old woman there. The old woman symbolizes the World or History or perhaps Civilization. The twin man and woman, both named Lily, that attend the old woman stand for the male and the female forces of civilization. The horde of little children symbolize human impulses or dreams that aren't yet clothed in ideas or form.
After the unicorn talks to Lilly in the garden, he becomes disgusted and says "I won't be back for 154 years"
The old woman dies and Lilly eventually takes her place. The old world dies and the new world is reborn.
Some of the animal symbols: The unicorn's horn is an antidote to poison, and represents healing of the world from biological or radioactive warfare. The eagle is the oldest being perched on top of Yggdrasil - the Tree of Life in Norse Mythology. The Eagle watches and remembers everything that's happened in the world, and then finally dies at Ragnarok - Götterdämmerung - the destruction and rebirth of the world. (Possibly the picture on the wall of the hero cutting down an eagle in the air, and slicing off it's wing refers to Finga, a hero who wore a single eagle wing on his helmet, who appears in Gaelic mythology and the poems of Ossian) The Black Horse is a symbol of Death by Famine. The sacrificed lamb symbolizes the death of the innocent or blameless.
Lilly recalls the mythic Lilith, the "first wife of Adam" , the owl demon who had little milk, who wouldn't defer to Adam, and defended her right to be his equal. Astrologers referred to the dark side of the moon as Lilith.
The twins that fight at the end could represent Líf and Lífthrasir (from the same root word as Life), brother and sister, last man and last woman on Earth that will repopulate the world after Ragnarok. Or maybe not, since we don't see any other humans after Lilly takes to bed, just teeming flocks of sheep and turkeys outside the house.