Banana fruits are, as the name suggests, fruits. They grow high on push fruit trees, and rarely can be found uneaten by animals on the ground.
Banshee of paradise seeds are attached on the stem opposite to the direction the plant is pointing, making it easy for the Na'vi to harvest them. Although the plant itself is deadly and toxic, the seeds are edible.
Bladder polyps are eaten by the Na’vi for their juicy salty taste, which is somewhat like a pickle.
Cycad seeds are soaked to remove nerve toxins and ground up to use as flour.
Dapophet leaves that are filled with water are collected and used by the Na'vi to drink from during travels.
Delta tree leaves and roots. The Na'vi have learned to strip off the lower leaf epidermis, which contains the poison glands, and harvest the tasty insides of the leaves. Roots that are non-poisonous are peeled, grounded up, and used for flour in cooking.
Spartan leaves are edible and are also used for making mats and food wraps.
Spiny whips eject small finger-shaped pieces of tissue, which can be collected and eaten.
Fungi
Fungus Soup can be eaten once boiled, but apparently it smells foul.
Symbiotic fungus on puffers is quite delicious and is used by the Na'vi for food. They are careful not to harvest too much off one plant in order to avoid destroying the equilibrium between plant and fungus required to maintain the health of both.
Dinicthoids, although dangerous, are a prized food for the Na'vi, who consider it a sign of courage to confront the fish.
Prolemuris offal is considered a delicacy among some Na'vi clans, and is used in food wraps.
Teylu is a main source of protein to the Na'vi. It is similar to a jumbo shrimp, being a grub, and is slightly sweet. Teylu is usually steamed, but the Na'vi also cook them with vegetables on a stick over an open fire, similar to Terran shish kebab.
Sources
James Cameron's Avatar: The Game - Ingame Pandorapedia articles on: Banshee of Paradise, Bladder Polyps, Hermit Bud, Lionberry, Puffer, Prolemuris, and Tapirus.