Are you sure the birds are starting the holes? or are they just taking advantage of an opening. My guess is that what you really have is... rats. They will cut into the oranges. Then the birds come along and take advantage of where the rats have opened up an orange.
My best way to deal with rats is cats. Unfortunately there is always person who thinks that because a cat is outside, that it is homeless. Then they catch it and "try to find it a home" But if you can get the neighbors to leave them alone, they can do some very find pest control. They also chase birds by the way. An outdoor cat will do a lot to help get rid of them.
Rats will usually get into the tree at night. One enterprising young man I knew got together with his friend and they got night vision goggles and a BB gun and camped out and hunted all the rats out. Can't do that in the city but that worked for them.
We lost our family cat about a year or so ago. In just a month we had a rat problem. We got 2 more from the pound, kept them inside until they felt at home, then they got to go outside. End of rat problem. One even catches a gopher now and then. GOOD kitty!

What you have is Gila Woodpeckers poking holes in your oranges.I haven't found anything to deter them aside from netting.This year seems to be bad for woodpeckers,I usually have a few damaged oranges but this year they have really made a mess.

well, at least they are pretty to look at.
I would think an airsoft gun might be just aggravating enough to keep them off without being deadly or dangerous. And of course cats.

i have had woodpecker trouble before.
try placeing orange christmass tree ornaments,orange styrofoam balls,while your fruit is small,green and developing.they will see it is not tastey

Curved billed thrashers will also peck holes in oranges and other citrus. Other birds take advantage of this and help themselves to the tasty juice inside.

You'll notice that once the birds start the initial hole, fruit flies and other insects will be attracted to the fruit. The fruit often falls off the tree after the holes appear because bacteria can enter the fruit and it begins to rot.

Rats (if you have them) will chew portions of the fruit. Birds however, create neat 1/2 inch diameter holes.

What can you do about this pecker problem with my oranges???

There is a product out there that we have used for years and it works pretty darn good. It is called bird scare or reflective tape. It comes on a roll like masking tape. Just cut a strip about 12-18" and tie it anywhere you need it. DON"T be skimpy. Then we just untie and move to another tree, grapes or patio over hang. Sold @ Home D, Warners, maybe Lowes.

Navymom ... they might be looking for moisture. Some source of drinking water for them might prevent some of it.

Hanging old CDs or glittery things in the tree also helps.