Please explain the way space is organized in Ithaca. What difference does this make to the way human beings interact with one another in those spaces?
If I understand your question, you are asking how the actions of the characters in the Odyssey interact with the space or location of Ithaca: how Ithaca fits in to the grand epic.
Most of Homer's first book, the Iliad, takes place near or on the Scamander plain (named after a Greek river god); Troy was located at one end of the plain, while the Greek ships were on the beach on the opposite end of the plain. Whereas the war had been fought by moving around, this part of the battle places the warring parties at two opposite ends of a flat piece of Trojan land that would serve as a stage of sorts, coming directly at each other. In this way the intensity of the plot moves more fluidly back and forth, establishing a greater sense of excitement in the battles. Fighting in the middle, no one has an advantage. The closer the fighting moves to one end or another, the better the advantage for the other side. In a sense, it is like football or soccer, moving into another team's territory. There is no indication that this ancient battle epic was duplicated anywhere else, real or imagined.
In that the story covers such a broad expanse of territory, it is important to note that the Odyssey deals with Odysseus' departure from Ithaca—where he joins other Greeks to battle the Trojans—and it is his gift of strategy and genius with the Trojan horse that allows the Greeks to be victorious. It is his twenty-year attempt to return home that pulls the action back towards Ithaca. As they say, all roads lead home, which is where the "final showdown" takes place in Odysseus' hall with the suitors. Even as the action of the epic takes the story far from Ithaca, inevitably it returns to its origins for the story's climax, and the resolution of the plot and related conflicts.
[Troy, Sparta and Ithaca were real places. Aeaea, Ogygia, and the islands of Aeolus (including the Sirens) are mythological in origin.]
Hope this is of some help.