Examine the roles of women and men in ancient Greek society as depicted in the story. For instance, Book I opens with Achilles' anger over having been denied Briseis, whom he considers his share of the plunder after a victory. Although women create plot devices like this, they possess no real power in Greek society, which could be further supported with more evidence from the story. On the other hand, men represent power and physical prowess, so Paris's failure to follow through with his initial challenge creates struggle between himself and his brother as well as with Helen. This attitude about men's roles could make an effective essay.
Religion and Belief
The role the gods play in the war and the Greeks' lives makes an interesting paper topic. Focus on how the gods instigate or further the conflicts, such as Apollo sending the plague that opens "The Iliad" and causes Achilles' loss of Briseis, or examine which gods seem to be the most powerful. A sample thesis could be, "The events of Homer's 'The Iliad' would have transpired very differently without divine intervention." Another possibility involves a character sketch of one of the gods, such as Athena, exploring what her actions tell readers about her personality and relationship with humans and other gods.
Glory and Honor
"The Iliad" emphasizes glory even if death comes with it. For instance, in Book IX, Achilles contemplates going home but decides to stay because leaving would cause a loss of fame. Similarly, you could write about how warfare seems to be the first choice for these characters rather than a last resort, that glory for these men comes from a heroic death. The meaning of "hero" in such context makes another potential topic. Consider if Achilles fulfills the requirements to be a hero: He turns the tide of the war but also is petulant and selfish. Contrasting the violence and concept of a good leader with that of other works, such as the Bible, would make interesting reading.
Part of what makes "The Iliad" a classic is the language Homer uses to express his ideas, so you could write about the symbols or the other literary elements and their effects of the story. For instance, Homer's similes, comparisons such as how a crowd of people "swarmed like bees," affect the tone of the story, clarify the situations and add depth. Homeric epithets -- phrases used for further description -- add the same clarity, such as "swift-footed Achilles" and "noble Achilles" in Book I. Your paper could discuss the reasons and benefits of such language in the work.