Odysseus alludes to the Trojan War when he sees his mother in the Underworld in Book X. He tells her that he's been wandering and experiencing "endless hardship from that day [he] first set sail with King Agamemnon bound for Troy, the stallion-land, to fight the Trojans there." The Trojan War was, indeed, a terrible ordeal, discussed at length in The Iliad. Odysseus fought in the Trojan War for ten years, prior to the start of his odyssey home, and the Achaeans only, finally, breached the walls of Troy and defeated with Trojans with the deceptive Trojan Horse (Odysseus's idea).
Odysseus sees many important figures from mythology in the Underworld. He describes the wives and daughters and mothers of quite a few famous men. He says, "And I saw Alcmena next, Amphitryon’s wife, who slept in the clasp of Zeus and merged in love and brought forth Heracles, rugged will and lion heart." With this line, he alludes to the story of Hercules. Zeus came to Hercules's mother in the form of her husband, so she slept with him, and she got pregnant with Hercules, son of Zeus and a demigod.
Moreover, Odysseus continues, "And I saw Megara too, magnanimous Creon’s daughter wed to the stalwart Heracles, the hero never daunted." Megara's story is terribly sad: Hera, in her anger at Zeus for his affair with Alcmena, Hercules's mother, drove Hercules insane so that he killed his wife, Megara, and their children. Hercules, when she returned him to his senses, felt so terrible that he embarked on a mission to cleanse himself of his awful actions.
Further, Odysseus sees "the mother of Oedipus, beautiful Epicaste. What a monstrous thing she did, in all innocence—she married her own son ... who’d killed his father, then he married her!" Another awful story: Epicaste receives a prophecy that her son would grow up to kill his father and marry her, so when she gave birth to Oedipus, she sent him away to be killed. However, the slave who took him away didn't kill him; he gave the baby away to a shepherd who served another royal family. When Oedipus grows up, he leaves home and an oracle tells him the same prophecy, so he vows never to go home again (not knowing he was adopted). In trying to avoid the prophecy, he inadvertently makes choices that allow for it to come true: he kills his real father and marries his mother, even siring children by her. When Epicaste finds out, she kills herself.