Odysseus is very clever when dealing with the cyclops Polyphemus. First of all, he lies to him when he is asked about his ship. He claims that it was destroyed. He does this so Polyphemus doesn't go out and destroy it himself. Then he tricks him into drinking the wine so that they could blind him. Lastly, he came up with the idea to hide under the sheep so that they could escape out of the cave without the blind Polyphemus knowing about it.
The one downfall to Odysseus character in this section is that he taunts Polyphemus. He gets carried away, and he boasts about what he has done and how he has tricked him and got away with it. Odysseus wants that fame, so he makes sure that Polyphemus knows his name and where he's from so that he can tell all who ruined him. This then allows Polyphemus to curse him. This curse is what creates such a hard trip home for him and the death of his crew.
One positive character trait that Odysseus shows with the cyclops situation is his cunning. He does this in many ways. First, Odysseus realized that the cyclops might not be friendly, so he lied about his ship being near shore and instead told Polyphemus, the cylcops, that his ship was destroyed by Poseidon. Later, Odysseus continues his cunning and tells Polyphemus a fake name, Nobody, instead of Odysseus. As readers, this doesn't seem cunning until later in the scene when Polyphemus is blinded and calls out for help: "Nobody's killing me." His brothers think that Polyphemus is alone and don't go to his aid, which is a great help to Odysseus and his crew's escape.
Another way that Odysseus shows his cunning is when he offers Polyphemus wine. Greek wine was very strong, and often had to be watered down. Odysseus gives him drink after drink, until Polyphemus passed out drunk, which was all part of Odysseus' cunning plan to escape the cave. Odysseus knew that Polyphemus would be the only one to move the boulder from the entrance of the cave, so he couldn't kill him, or else they would all be stuck in the cave. So Odysseus came up with the idea to blind Polyphemus. Odysseus and his men sharpened a stake and put it in hot embers and Odysseus and his men rammed it into Polyphemus' eye. After Polyphemus opened the cave entrance, he blocked the exit with his body and felt around for the men trying to exit. Odysseus shows his final example of cunning with their escape. He noticed that the sheep were escaping, so he tied each man to the bellies of three sheep at a time and they all escaped to their ship.
The Odyssey centers around the theme, brain versus brawn. This theme is most prevalent during this instance with the Cyclopes. It is nearly impossible to deny that Odysseus acts brilliantly in this situation. The Cyclops traps Odysseus in a cave which he seals with a giant boulder that no mortal man can lift. Odysseus cannot kill the Cyclops because if he does so, he will never be able to escape from the cave. Instead he tells the Cyclopes that his name is Noman and gets him drunk on wine.
When the Cyclopes lies down for the night, Odysseus and his men sharpen a pike which they use to pierce the Cyclope's only eye. The Cyclopes, blinded, runs outside to tell his neighbors what has happened but when asked who blinded him he can only respond "Noman blinded me!" The next day, Odysseus ties his men to the bellies of the Cyclopes sheep, so when the Cyclopes lets out his sheep to the pasture, Odysseus and his men escape.
But as Odysseus sails away, his pride overcomes him and he shouts his real name to the Cyclops. The Cyclopes then prays to Poseidon to curse Odysseus. This prevents Odysseus from returning home for ten years.
So in answer to your question, Odysseus strength was his brilliance in escaping the Cyclopes and his weaknesses were both in his pride and in his gluttony. It was Odysseus's gluttony that lead him into the Cyclops' cave, where he feasted on cheese.