This is an excellent and insightful question. Moreover, the coordination of the external and internal character of Odysseus is complicated, because Odysseus is known for his cleverness and deceit (in a good way). Let me explain.
Odysseus, like all heroes, is brave, courageous, and noble in his birth. He is the king of Ithaca. He also can wield a sword and do his part in warfare. In other words, he is no slouch in battle. In this regard, he has the qualities of what you would expect in an ancient Greek hero (arete). But, he has something extra; he is a man of many twists and turns. In Greek the word is "polytropos."
This last point makes Odysseus use deceit to overcome his enemies. For instance, instead of fighting Polyphemus head on, he pretends to be his friend to gain an advantage. Similarly, instead of fighting the suitors in Ithaca in a pitched battle, he disguises himself, plots and traps them to their death. He does the same to end the Trojan war with the artifice of the wooden horse.
The point is that often times Odysseus changes his outward appearance to gain the upper hand against his foes. So, his external characteristics always changes depending on this situation, but internally he is the same brave and courageous hero of the Greek world.