Which postive and negative character traits does Odysseus demonstrate in his adventure with the Cyclops?

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.