A strange and fascinating question. Can I include brief references to the Trojan War as well?
The twentieth and early twenty-first centuries are marked by a number of movements: development of state power, development of advanced technologies, violence and mass slaughter, mass population growth, new explorations of the world, rising spirits and loss of spirits.
You could link most of those to the Odyssey. Many warriors went to war. The wars took longer than we thought, and some warriors took decades to get home. (Some Vietnam era soldiers are still MIA.) Immigrants must take years, and strange voyages, to find new homes—think of the boat people. Those are like Odysseus.
Many face challenges they cannot survive through force. I think of the Jews trying to slip past Nazis to survive the Holocaust; they could be fighting Polyphemus.
The lotus eaters compare to mass drug use in society—and to mass television watching.
Our leaders must steer courses through many threats on all sides, like Scylla and Charybdis.
Astronauts went to strange and magical places, like those Odysseus found on his voyage.