(Click the character infographic to download.)
Think of Odysseus as the Dr. Ian Malcolm of The Iliad. Ian Malcolm spends the entirety of Jurassic Park stealing scenes, but it's not until The Lost World that he gets to be the star of the show. In the Iliad, Odysseus is the brains to Achilleus' brawn... but it's not until The Odyssey that we get to see him take center stage.
Even though he does not appear in many scenes, Odysseus's role in the Iliad lays the groundwork for a subsequent tradition (including the Odyssey and the non-Homeric poems of The Epic Cycle) that portrays him as a wily trickster. From these works, we get a picture of Odysseus as an alternative kind of hero to Achilleus—one who survives by his wits.
The most obvious case of this in the Iliad is Book 10, the longest stretch in the poem that focuses on Odysseus, in which he and Diomedes lead a night-raid that takes them first into no-man's-land and then behind enemy lines, where they steal the horses of the Trojan ally King Rhesos.
Some scholars, however, believe that Book 10 was not originally part of the Iliad, but was written later by somebody else and then stuck in where it would be inconspicuous. If this is true, than this episode can't be an inspiration for the later tradition—it was part of the later tradition!
Whether or not this is the case, the fact remains that the Iliad always shows Odysseus as a smart guy. You can see this, for example, in his advice to Agamemnon not to sail away for home in the middle of the battle, which he justifies with an insightful discussion of the psychology of teamwork. Interestingly, on another occasion, we see Odysseus running away from a battle, and disregarding Diomedes's cries to turn back. This is something Achilleus would never do.
Do we interpret this as a lack of courage? Or is it just another sign how Odysseus is able to think beyond the warrior code and realize that sometimes you just have to back down?