What is a strong thesis statement for how the world of the Odyssey of Homer looks at masculinity by portraying Odysseus?
This is a great question. As you probably know, a thesis is the most important part of a paper. In light of this, let me give you a few suggestions.
First, you can say that Odysseus, as the protagonist / hero of the work is the embodiment of masculinity. In view of this, you can then pick a number of traits that he possesses and argue that these traits are what constitutes manliness. If you go this route, you can mention his cunning and his military prowess. These are probably the two greatest traits that Odysseus possesses.
Second, you can also compare Odysseus to Achilles. This can be an interesting paper. There is overlap between these two heroes, but only Odysseus has the quality of deception or cunning. So, you can write a paper on the importance of cunning as a masculine idea in the homeric world. This is also an insightful paper, because in our modern age, cunning is not very masculine at all.