What is causing these deformed apples?
This appears to be the damage caused by plum curculio, a species of weevil.
The plum curculio weevil, Conotrachelus nenuphar, becomes active in May and the females lay eggs in apples, pears, plum, Beach plum especially, quince, peaches, and cherries. The adult plum curculio is a small, hard-bodied, brownish-black snout beetle mottled with white and orange areas. It has 4 prominent black humps on its top surface. It is about 6 mm long, has a long snout, the end of which bears chewing mouthparts. The insect overwinters as an adult under debris. A small cavity is made in the fruit for the egg; then a crescent-shaped cut is made adjacent to the egg pocket. The early feeding and egg-laying punctures can cause marked scarring and severe deformity of the fruit. Larvae hatching from the eggs feed inside the fruit until they are fully grown. Larval feeding in apples can cause distortion of the fruit.
Control: If you are seeing this damage on the fruit, it is already too late to treat. If you need to protect home fruit, an application of Imidan can be applied. You have to kill the adult females before she deposits eggs into the fruit. If you miss this application, the crescent-shaped damage will appear on the fruit in late May and early June. Damaged fruit will often fall off the tree.
* Hang plastic traps (empty 2-liter soda bottles) filled halfway with molasses, vinegar, and water from tree limbs when petals fall in spring.
* Removed infested fruit from the tree.
* Lightly cultivate soil under the tree before the flower buds begin to swell in spring--this disrupts/kills overwintering adults.
* Keep trees pruned and open in the center -- curculios prefer deep shade.
* Lay a white sheet under the tree, tap branches with a padded stick, then capture and kill adults when they drop to the ground.
Here are some photos. Notice especially the heavily infested fruit photos down the page: http://content.ces.ncsu.edu/plum-curculio/