Pillbugs and Sowbugs (sometimes called Rolly-Pollies) are often accused of making holes in strawberries, but from what I understand, they will only eat strawberries if another critter has already made a hole in the berry. Their God-given role is garden garbage man. A good organic garden should have lots of pillbugs or sowbugs, so it's best to leave them alone and discover what critters are creating the initial holes in your strawberries. That said, you can reduce their damage to strawberries by reducing soil moisture as the berries ripen. Sowbugs need moist soil to survive; dry soil deters them.
Sap beetles and millipedes are two more insects attracted to already damaged or overripe strawberries. Taking care of the initial strawberry-eaters - and being sure to pick berries promptly when ripe - will keep sap beetles and millipedes at bay.
It's not unusual for birds to eat strawberries. Fortunately, it's not difficult to deter birds. The best method is to cover the strawberry patch with bird netting (readily available at garden centers and home improvement stores) or tulle fabric. In the past, I've used sticks found in my yard to support the netting, along with twisty ties from store bought bread to hold the netting to the sticks.
There are many other ways to deter birds, but few of them work consistently. Some people hang old CDs or DVDs from string, hoping their movement in the wind (and the sunlight flashing off them) will scare birds away. But in most cases, this only works until the neighborhood birds get used to them. Having an outdoor cat or dog is probably a better deterrent.
This is likely the culprit in my yard, since I've had a huge infestation this year (much to the delight of my slug- and snail-eating hens!). Just as strawberries ripen, slugs are notorious for chewing holes in them. If you have mulch - especially organic mulch like straw - around your strawberries, this gives the slimy things a perfect hiding place. Theoretically, coarse mulch like bark should help keep slugs and snails at bay, but in reality, I've not found this a deterrent.
Hand picking (especially in the cool of the morning or after dark) is a good way to limit the number of slugs and snails in your yard, but the best cure is usually laying down slug and snail bait. Sluggo is safe around children and pets (even if the pets eat the dead slugs or snails); for those who don't have to worry about this, Corry's is just as effective, but cheaper. Or, if the strawberries are in a raised bed and none of the leaves touch the bed frame, lay copper strips on top of the frame. Slugs and snails can't cross it.
Earwigs leave holes very much like the holes slugs and snails leave in strawberries. The only way to know whether you're dealing with earwigs or slugs is to look for a slime trail (in which case the culprit is slugs or snails) or go out in the evening and see if you can catch slugs or snails doing the munching. Like slugs, earwigs love organic mulch.
Catch earwigs by rolling up a piece of newspaper, then dampening it. Set it near the strawberries and in the morning, wrap the newspaper up in a plastic bag and dispose of in the trash. Or burn the paper.
If you're strawberry pest problem occurs not on the berries, but on the leaves, roots, or crowns, be sure to check out University of Nebraska's .PDF, "Strawberry Pests."