Odysseus would have a map to represent that hard work and persistence pays off. The map would remind him of the 10-year journey he took to get home. He would always remember that in order to reach one's goals a person must never give up but keep trying his best.
Picture of Argus
This picture of Argus, his dog, would remind Odysseus of the importance of loyalty. In addition to Argus, only Odysseus's wife, son and sheepherder Eumaeus remained loyal. Through his absence, Odysseus learned that in order to inspire loyalty one must truly care for others and not just about themselves.
The wine chalice represents to Odysseus the importance of using your head to find a solution. On the island of the Cyclops, Odysseus brought with him the nectar of the gods, which he uses to get the Cyclops drunk and stab his eye as part of his escape plan. Odysseus learned that it's not always about brute strength, but that one should use their intelligence to solve problems.
Statue of Athena
The statue of Athena represents the idea that no one can do it all by his or herself. During his journey, Odysseus had to learn to look to the Athena and the other gods for help. He asked Zeus to protect him when he was all alone going past Scylla and Charybdis the second time. He could never have survived without help, and he acknowledges that help when retelling his story. Odysseus came to realize that success comes from asking for help and showing gratitude, rather than being arrogant and seeking personal glory.