Does Odysseus kill Orsilochos in The Odyssey?
No, he does not. Orsilochos is mentioned in Book XIII when Athena comes to Odysseus in disguise and reveals to him that he has successfully returned to Ithaca. Odysseus, because he knows he is returning after a very long time, wants to find out more information about what has happened in the interim during his absence. He shows his wily and cunning nature through his reluctance to announce his presence immediately, rather waiting to scout out the territory first before announcing his presence prematurely and placing himself in a potential situation of jeopardy. Because he does not recognise the goddess Athena, he therefore tells her a lie about his background:
I have left as much more behind me for my children, but am flying because I killed Orsilochus son of Idomeneus, the fleetest runner in Crete. I killed him because he wanted to rob me of the spoils I had got from Troy with so much trouble and danger both on the field of battle and by the waves of the weary sea...
This, however, is a "lying story" that Odysseus tells Athena, and is not based on any true event. Although Odysseus certainly was at the Trojan War, he did not kill any man called Orsilochus as a result of his desire to protect his loot, and is only coming up with this story now to protect his identity whilst he works out what has happened in Ithaca during his absence.