Of the 7 Greek virtues, which does Odysseus show in Book XIII of The Odyssey?
In Book XIII Odysseus does a lot of complaining, which certainly is not a virtue, but in the midst of it he shows the virtue that Greek champions and heroes are most noted for, that being courage. Of course the champions and heroes always had help from the gods and the case Odysseus is no exception for Minerva, the niece of Neptune (who did not forgive Odysseus for blinding his son in battle and swore his vengeance against Odysseus (watch out whom you offend...)) had helped Odysseus all through the Trojain war and had begun helping him once again after a brief hiatus, as she explains to Odyesseus.
After Odysseus and Minerva stow his treasures in the cave and while she is filling him in on the situation at his house so that he won't go unadvisedly in and wide up murdered on his own threshold, Odysseus rises to the need at hand. He starts by seeking Minerva's aid whereby she puts courage in his heart as she did on the day that the Achaeans successfully "loosed Troy's fair diadem" and conquered the city. The virtue that Odysseus displays is courage, which is also called fortitude, and, in keeping with beliefs and customs, he attributes his courage/fortitude to Minerva who is his patroness and helper.
[Note: There are generally said to be four Greek virtues and three Christian virtues, which together make up the Seven Cardinal Virtues of the Catholic Church. The Four Greek virtues are said to be Fortitude (courage); justice; temperance; and prudence. The three Christian virtues are said to be faith; hope; charity, which is interpreted as love. Together these comprise the Seven Cardinal Virtues of Catholicism. In this usage, cardinal means central or pivotal, meaning the virtues upon which every other virtue depends and/or is sprung.]