What would a meeting between Gulliver from “Gulliver’s Travels” and Odysseus from “The Odyssey” be like?
If the two met, Gulliver might be a traveling storyteller in Homer's style, a man who brings tales from far off lands. In Homer's time, tall tales were more likely to be believed, since so few people had done traveling to other countries and cultures, so Gulliver would be taken at his word. Odysseus would probably entertain Gulliver in his hall and Gulliver's stories would be discussed among the gods and heroes around a meal, possibly culminating with Gulliver showing off uniquely European customs or skills.
The two characters would have little in common beyond their shared travels, which themselves would be strange and different enough to fill conversation. This is, of course, assuming that Gulliver is not immediately killed for heresy; he would not believe in the old gods and would have no compunctions about speaking his mind.
In any written meeting between fictional characters, every writer will write them differently. If you look at the several finished versions of Charles Dickens's Mystery of Edwin Drood, for example, they range from locked-room mystery to comedy to horror as each writer gives the characters their own spin. A writer of fantasy will write the characters in a more classic vein than a writer of modern thrillers.
In this case, Jonathan Swift was a writer of broad satire, while Homer wrote epic myths; Swift's writing leans heavily on puns, wordplay, and comedic interpretations of European government, while Homer wrote about the myths and legends of his time, some of which were taken as fact, and so was more serious in his style. The two writers would clash on every level, so one or the other would have to write the story for it to have any coherence.
In Swift's version, Odysseus would likely be portrayed as a delusional old man, a veteren of wars far past his prime, living like a king and telling his tales of glory while Gulliver listened. Gulliver, for his part, would think about how Odysseus's life and the state of his kingdom compares with European culture; in turn, Gulliver's explanation of his home and governmental structure would baffle Odysseus, who comes from a simpler time.