Is he on antibiotics for the skin infection he has? With the oily, dander, smelling issue you mention, it sounds like it could maybe a staph, or possibly yeast infection which can be contagious to people and part of the cause of the human 'allergies'. Even if the initial cause was 'allergies', his scratching can cause a skin infection.
How long since the dog has seen the vet? Did the vet do any skin scrapings or cultures? As Karen mentioned, is he on any special shampoo? Is he on a special hypoallergenic or restricted diet for food allergies? Has he been tested for what 'allergies' he has?
I just somehow doubt that the whole family is suddenly becoming allergic to the dog without another reason being involved like a staph or yeast infection. Not saying it can't happen, just doesn't sound likely.
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