It's time to get your mix-bred dog (adding a silly name doesn't make him anything else) checked by your vet. If he's that itchy, he must be miserable. Good skin and coat comes from WITHIN so any amount of external treatment may do nothing, as you've found. If you are feeding a cereal-based food, switch. Find something that lists meat, or fish as the first, main ingredient.
Secondly there is a steriod injection that can be given which lasts for roughly 4 months - slow release. But your vet should be able to examine and correctly diagnose what's going on.
Excessive shampooing will only make a dry skin situation worse so you should stop doing that.
Re fleas, even if the dog is free of them, once the skin is inflammed, it will take time for itching to stop.