My garden has a huge problem with earwigs, Snails, and Slugs, and many of my plants are dying. How can I effectively eliminate these pests.
Slug pellets will take care of the snails and slugs - earwigs are a different matter, they usually nibble on flowers overnight and an upturned pot on a stick or cane with straw in it near their favourite flowers should mean they're in there first thing in the morning. You empty the pots and straw into a bucket of water or the ground and stomp on the earwigs.
Neither of these pests will actually kill plants, although snails and slugs might demolish some plants just as they start appearing above ground by eating them immediately and repetitively till the plant gives up - hostas for instance, or delphiniums, certain vegetable plants, early in spring may suffer this. Otherwise, they don't usually kill plants, just damage them by eating them, and earwigs don't either, so more information is required if many of your plants are dying - like what the plants are, where they're growing, etc.
Ducks are best for snails and slugs, but chickens will work too, and will pick up the earwigs in a heartbeat. Depending on the size of your garden one laying hen may be enough. This will require some short term protection of new plantings, but will actually fertilize your flowers and other shrubs.
Another great technique that I have used with success is to half bury a bowl and pour a bit of beer in it, say half a can (I drink the other half, but if you don't like beer pour it all in). The next day or some days later you can empty the bowl and pour fresh beer in. You are likely to find slugs, snails and earwigs (and other critters) floating dead in the beer bowl. They can't swim but must get thirsty. Good luck!
Having given the chicken route a try, I'd only suggest it (and likely ducks as well, though I haven't tried them) in the "Bird moat" method where you ring your garden with a bird run, so critters trying to get in or out need to cross the "moat". Chickens certainly eat slugs and snails, but also scratch (dig things up) looking for other stuff, and eat tomatoes, tomatillos, and various other produce. And, of course, they roost at night when the critters you want eaten are most active. And various predators want to eat them, which can be both a hassle and disturbing.
If you do that, shelter/trap boards in the bird run can be highly effective - critters hide under them, you turn them over, the birds soon learn to be there when you turn them over to get the exposed critters. You can also use those in the same manner as the earwig trap already described (which the birds will help out with if you have birds) without poultry to eat the beasties if you just kill them yourself.
Regarding on how to reduce the population of earwigs, I can suggest something that worked for us really well:
Pick a small plastic tray without holes in it, something like plastic vegetable tray or fish can.
Fill it with Olive oil up to 1cm deep. Add some soy sauce as it icreases the smell and attracts more earwigs.
Put this tray overnight under the plants which have the biggest problem.
In the morning you should see many dead earwigs in that trapping tray. You can pick those out and throw them away then set the trap for the next day until you are happy with the result. Earwigs are good at eating alphids so you don't want to get rid of them entirely but also you don't want to find many of them inside your favourite plant buds. Good luck!