No, not the puffy things you get on your skin. The little critters that dig up your yard. I haven’t actually seen them, but there are suspicious tunnel type holes in the garden. And my dog has uprooted several plants, trying to find them.
The people next door recently put mothballs in their yard, and I’m wondering if that drove the wildlife into my yard.
Any advice would be appreciated.
rent a copy of “Caddyshack” 
no experiance with em, sorry! I only deal with coyotes, jackrabbits and wild horses.
There is nothing “secret” or “special” about 1,000 Island Dressing.
Moles and moths? Bummer.
Here’s a link to some good info:
I once heard a radio garden show say that moles are drawn to a food source, especially grubs. If you treat your lawn for grubs, the moles might be encouraged to leave, or at least find it harder to multiply.
We have a full blown infestation of moles in our backyard – furrows and depressions everywhere from collapsed tunnels. They never bother our gardens, though, and we let them stay, figuring its an ecologically friendly way to keep the grubs under control 
I had one under the cement pad that was going to be a garage. But I never saw any others. I wonder if a zoo could give you a humane cure for the problem.
I always heard that if you pour hot water in their holes, it will get rid of them. The hard part is finding someone to hold them upside-down while you do it 
Mom used to put those plastic windmill flowers that look like sunflowers around the garden. Supposedly, the vibrations when they they turn in the wind are transferred into the ground, and drives the moles away. No idea if it really worked, but we had mole tunnels all over the yard, except in the garden. YMMV.
You could try pouring tabasco or hot sauce into the openings, and spreading it around the borders of the garden.
Good luck.