There are a number of sources from which Odysseus gains power in the course of the story. The first and one of the most constant sources is his great physical strength. Stories of his strength during the war have helped to draw his men to him and he exhibits this strength repeatedly during his quest to return home. He survives all kinds of terrible assaults on his person and, aided by the gods, uses his immense strength to help his men.
He also draws strength from a confidence in both his strength and his cunning. At times this arrogance leads to trouble, for example when he escapes from the Cyclops and then mocks him cruelly, further enraging the father of the Cyclops, Poseidon.
He is also aided a great deal by several of the Gods but in particular by Athena who works behind the scenes to encourage Telemachus to go on a rescue attempt and also helps Odysseus to return home and then intervenes with the families of the suitors to help Odysseus establish himself again as a powerful ruler in the land.