Why do you think the tale of Odysseus, as detailed in The Odyssey, has had such long lasting appeal since it was initially composed?
I think the story just speaks to people on a very basic level-- it's truly "got it all". A hero, monsters, a quest, women, etc. It's fun to read even though it's difficult to understand at first.
There are any number of reasons why the story continues to resonate with readers. First, Odysseus is a classic hero in the tradition of Beowulf or Luke Skywalker. He had a great quest to undertake, and that quest forces him to face the worst in both the world and in himself. Rather than giving up, Odysseus overcomes both his own fears and desires and the hatred of the world. That sort of story is very empowering in that it shows one of us... a human... overcoming that which seems overwhelming.
Joseph Campbell writes on why myth still continues to capture our imagination, and he wrote, "The function of mythological symbols is to give you a sense of 'Aha! Yes. I know what it is, it's myself.'" Odyesseus gives us this. If he can overcome all that he has overcome, we can survive high school and mean gossip and being overwhelmed with homework, all of which feels equally overpowering for us.
Indeed it has a long lasting appeal if we realize that it was composed by Homer more than 3000 years ago.
And this is true for many reasons.
First, it's the triumph of man over nature, the ingenuity and the resourcefulness of a human being combating misfortunes of life, his willingness to go above and beyond, the patience and the faithfulness of a man towards his wife and vice verse and a lot more... It's when big obstacles become little confronted by a man's inventiveness. It's when the myth becomes part of life.