Much of what Odysseus does in The Odyssey shows how clever and crafty he is. However, he is one of the most heroic soldiers of the Trojan War. Had he not been physically strong, he could not have held such respect among his men.
The best example of Odysseus's physical strength comes with the test of the suitors by Penelope. Odysseus is the only man strong enough to string the bow (although his son, Telemachus, comes closest). After his identity is revealed, Odysseus slays every man in the room. He is indisputably the strongest of all the men who want Penelope, not simply the smartest.
While it is true that Odysseus's defining traits are his cleverness and cunning intelligence, he does exhibit physical strength. To be a proper Homeric Hero, it is necessary that one is extremely strong. Odysseus usually uses his physical power to supplement his mind, not as his first approach. It is always a given that he is a strong man, because of the fact that he is a war hero and a king.
Here are some other places in Odysseus's journey in which his physical strength helped him:
-He drives a stake through the eye of the Cyclops Polyphemus, blinding the giant, and thus allowing his men to escape.
-While his entire ship and his entire crew are drowned by the whirlpool monster Charybdis, he clings on to a fig tree above the water and is the only one who survives.
-He takes part of a pentathlon while under Alcinous and Arete's care in Phaeacia.