Is your itchy pet getting EFAs? 
Essential Fatty Acids (EFAs) are essential for healthy skin. Omega-3 EFAs are the ones to aim for to help reduce itching, shedding, and redness. They not only nourish the skin, they reduce inflammation.
Even though dry pet foods list EFAs as part of their formula there isn't enough to be useful. More importantly, by the time it goes through the high-heat processing it has become degraded and no longer healthful.
It should be added directly to the diet in the form of liquid fish oil. Some plant oils, like flax, also contain high amounts of Omega-3s, but in a form that dogs and cats have to convert in their bodies, which makes them much less effficient.
Why Omega-3? Most of us, and most of our pets, do not get enough Omega-3 fatty acids through our usual diet. We do get plenty of Omega-6 fatty acids, though. Olive oil, for example, is high in Omega-6 fatty acids, so adding olive oil to your pet's diet won't reduce inflammation; adding fish oil will.
Pets with serious and chronic skin problems will need more than just fish oil in their diet to resolve their discomfort, but it is certainly one of the first supplements you should add.
Dexter's offers several options for cats and dogs: Iceland Pure, Animal Esssentials, and Nordic Naturals.
As with all new supplements start slowly at one-fourth the recommended dose and work your way up to the full dose over a week or so. Discuss dosage with your vet or non-vet practitioner, as many animals with chronic inflammation benefit from larger-than-normal doses.