The first convention would probably be the focus on the actions of the hero against the backdrop of important historical events. The hero's actions, at least in part, shape the outcome of these events.
One Internet source (http://english.tjc.edu/greekromanepic/conventions.htm) cites a number of other conventions that might apply:
Epithet: The hobbit Frodo is called by other names, such as The Ring Bearer.
Long and formal speeches by characters
Gods (or wizards and the evil disembodied force of Sauron, who are all clearly more than human) intervene
Values of civilizations
On a side note, I think it might make more sense to compare The Lord of the Rings to the Germanic epic Beowulf. There's nothing wrong with making the comparison to The Odyssey, but Tolkien was clearly influenced by the Germanic tale.