Let's test each possibility of who is telling the truth. Case 1: Hawk's statement "the owl did it" is true. Then Sparrow's statement "the hawk did it" is false. Eagle's statement "not me" is false (meaning Eagle did it). This is a contradiction. Case 2: Hawk's statement "Sparrow is lying" is true. This means Sparrow's claim "Hawk did it" is false. So Hawk is innocent. Hawk's other statement "the owl did it" must be false. So Owl is innocent. Eagle's statement "not me" must be false. This means Eagle is the killer. This scenario is consistent.