Eat. According to the Woodpecker Encyclopedia, the foods that woodpeckers eat include: acorns, ash borers, termites, ants, sap, wasps, pecans, etc. Insects are the woodpecker's favorite, as are nuts, fruits and acorns. A common name for birds in the family Birds, order Pygniformes, and family Woodpeckers. It is a common resident bird. The species widely distributed in China include green woodpecker and spotted woodpecker.