What are three examples that show Odysseus has no supernatural powers?
When Odysseus is adrift in the ocean, before he reaches Phaeacia, Poseidon sends terrible storms in an attempt to drown him (as revenge for blinding his Cyclops son, Polyphemus). If Odysseus has supernatural powers, it seems likely that he would use them here to keep himself alive. However, he does not, and so Ino, a goddess, takes mercy on him and gives him an "immortal veil" that prevents him from drowning if he takes off all his clothes and wears only it.
In this same book, Odysseus grasps a large rock for support, and clings as to it as tightly as he can. However, as another giant wave covers him, he is pulled from the rock, leaving pieces of skin behind, just like a "polyp [that] is torn from out its bed, about its suckers clustering pebbles cling." If Odysseus had supernatural powers, he would likely not have been torn from the rock by such a force. If he were superhuman, he would have been able to hold on.
Later, when Odysseus is telling his story to Alcinous, king of Phaeacia, he describes his crew's earlier encounter with Polyphemus, the Cyclops. This monster failed to offer them the hospitality which was customary, and, not only that, he actually ate several of the crew before Odysseus hatched a plan to escape. If Odysseus had supernatural powers, I'm quite sure he would have used them against Polyphemus to prevent his eating Odysseus's crew members.