Itchy yorkie poo! Any suggestions?

Often it's related to their diet. Do you have him on a good meat-based food? No wheat, corn, soy, non-specific byproducts, aftificial colorings, or artificial flavorings? If not, get him switched over (slowly, to avoid stomach upset). There's lots of good brands on the market, including Merrick, Innova, Canidae, California Naturals, Go! Naturals, Taste of the WIld, Wellness, Solid Gold, Orijen, Acana, and many, many others. If you're on a tight budget, look at Costco's Kirkland dog food. Much better than most foods on the market, and extremely affordable. I'd also supplement with fish oil to improve skin condition. With a small dog, one caplet a day would be appropriate. Pet stores sell it, or you can give plain human fish oil gel caps instead. If the itching doesn't significantly reduce to normal levels within a few weeks of the diet change, I'd have the vet check him over for something like mange mites.

First, stop bathing him. If you are bathing him more than once a month that is too much and you will only make the problem worse by over drying his skin and coat. Over bathing a dog can be so drying and damaging that it can cause severe itching and even skin irritation and pain.

Next, take him to the vet to rule out mange, then evaluate what you are feeding him. Eliminate corn, wheat, and soy from his diet as they are some of the most common allergens in dogs. Make sure the first two listed ingredients in his food are meat or meat meal from an identified animal.

Alternatively, put him on a bland diet for a week to see if anything changes.

One part cooked chicken OR boiled, thoroughly rinsed hamburger
Two parts cooked rice OR oatmeal
A tablespoon of pureed pumpkin or sweet potato (no spices or sugar)
A tablespoon cottage cheese OR active culture yogurt

Also consider environmental allergies.

What you have is a Yorkshire/Poodle mix. Probably poorly bred, because reputable breeders don't breed mutts. And with these mutts, comes health problems. See your vet for an exam and proper medications.

You might be bathing him too often. Our Yorkie always itched for about 3 days after a bath and then it went away. We use pert dandruff shampoo on her now and it seemed to help. All the dog anti itch shampoos were worthless. We tried them all.

I would bet it's a food allergy and all the bathing is making it feel worse.
It's common and when you get her on a different food it will stop in a about
a week. We had the same problem and put her on Blue Buffalo for small
breeds. The itching stopped and her coat showed a great improvement, even
grew longer and she is an older dog.

More brushing and less shampooing might help a bit.

Brushing would make his skin healthier while getting rid of dead hair, dirt, body odour etc. Then less washing is required. Too much washing could cause itching.

it could be many things causing the itchiness. could be his diet, bug bites, skin infection, mites, mange, ticks, sand flies, mosquitoes, dirt, lice, fleas...the list goes on. frontline helps prevent fleas but is not guaranteed to stop them. ask your vet what they recommend. try using an all natural oatmeal based shampoo for dogs and puppies and see if it helps at all.

You answered your own question, "We've tried bathing him in all kinds of different itching dog shampoo" You are bathing this dog to much.
Take him to a vet and have the vet check for allergies and have him recommend a proper shampoo to bath him in. And then only bathe your dog every 6-8 weeks, with daily brushing.

Is he chewing at his back end at all? If so could be blocked anal glands easily sorted. Id recommend a vet check as it could be an allergy, if hes on a good diet he shouldnt need treating for dry skin.
Qualified Veterinary Nurse

Get some dandruff shampoo for dogs. See if that works. If it doesn't take him to the vet and they might give him some special lotion or something.