I read all of the Odyssey and about eight books of the Iliad when I was in college. I still have my vocabulary notebooks and my copy of Cunliffe’s Lexicon of the Homeric Dialect, since I always intended to go back and finish. I can still follow the syntax without much difficulty, but my vocabulary is a wreck.
The Odyssey is much easier than the Iliad in vocabulary and syntax, and many modern readers find it more appealing in various ways. Joyce wisely modeled his modern-day hero on Odysseus, not Achilles or Hector.
I never had to read any but my mother did. She went to school in a small town in TN and got a much better education than I did.
I liked the Iliad better. I think there is more real history lurking in it.