How is Odysseus powerful in The Odyssey?

Odysseus is powerful in three ways: first, because he is physically strong; second, because he is intelligent; and third, because he learns self discipline.
Odysseus is stronger than almost any other man and is tireless to boot. He has limbs like "iron," and he never fatigues. He doesn't just give orders and let other men do the grunt work: he leads the way. At the end, he is the one who can string (pull back) the bow and shoot it through twelve arrowheads. He is muscular, high energy, and strong as an ox.
Odysseus also knows how to use his brains. He is the mastermind behind the Trojan horse. That strategy allows the Greeks to trick the Trojans and win the long war. He also outwits Polyphemus, the Cyclops who wants to eat all his men.
As many have noted, Odysseus changes and grow internally during the course of this epic. He learns the hard way he shouldn't have bragged to the blinded Polyphemus and revealed who he was. This blunder allowed Neptune to wreak revenge on Odysseus and his crew. By the time Odysseus arrives home, however, he has learned his lesson. He is willing to accept the disguise Athena contrives for him of a humble beggar, and he doesn't let his true identity be known until the right moment, at which time he uses his great strength to kill his rivals. His self-discipline helps him regain Penelope.

Odysseus displays his power in several ways. We see his power when he overpowers the three men from his crew who desperately want to remain with the lotus eaters because they ate the lotus fruit. He knows that they, in their hearts, want to return home, so he muscles them back to the ship for their own good. 
We also see Odysseus's power when he clings to the rock and survives the terrible storm Poseidon sends to kill him after he's departed from Calypso's island. He clasps the rock so hard that he actually leaves behind some skin from his hands when the waves crash against him and force him off. 
Further, we see Odysseus's social power when he convinces his men to help him blind the Cyclops, Polyphemus, as well as the physical power such an act requires. This episode also helps demonstrate the power of Odysseus's quick mind when he tells the monster that his name is "Nobody" so the Cyclops will not be able to identify him to his friends when they rush to his aid.