You can read the Odyssey is many different ways. Moreover, I am sure that people will find newer ways to read it in the future. Let me give you a few different ways in which to read the Odyssey.
First, you can read the Odyssey as a source for history. In this approach, you read the text to find historical information about the time in which Homer lived. For example, you can look at little details like whether they used chariots and how they used these chariots. With this information, you can compare what we know of various historical periods to make conclusions. Examining a text for historical details can yield some very insightful points.
Second, you can read this text from any number of literary approaches. For example, you can trace themes. You can trace the theme of cunning, or the theme of faithfulness, or any number of other themes.