I'm sorry to hear of the with your dog, Linda. The smell of old cheese (also described as dirty gym socks) is pathognomonic (particularly indicative) of seborrhea in our dogs.
Clinical signs of seborrhea may include a dull, dry, lusterless hair coat, excessive scaling (dandruff), follicular casts, scaly and crusty seborrheic patches and plaques, and greasy, malodorous skin. Most of the body is involved to some degree, with interdigital areas, perineum, face, axillae, ventral neck, abdomen, and skin folds usually most severely affected. Pruritis (itchiness) is mild to intense, and ceruminous otitis externa (oily external ear canal inflammation) is common. Secondary skin and ear infections with bacteria and Malassezia (yeast) are often present and will contribute to his pruritis (itchiness) as indicated by his scratching, chewing, and licking himself. Here's a primer how seborrhea is addressed:
1) Ensure good nutrition. A commercially balanced dog food that meets AAFCO requirements should be fed. You should find the AAFCO statement on the food label. Perhaps the new food is contributory.
2) Any secondary bacterial and Malassezia skin and ear infection should be treated with appropriate topical and systemic therapies. Periodic treatments or long-term, low-dose maintenance therapy may be needed because these dogs are susceptible to recurring infection.
3) For symptomatic control of ceruminous otitis, long-term maintenance ear care is necessary. Ear treatments with a multimodal therapy (consult with his vet) or ear cleaner should be administered to both ears every 1-7 days to control cerumen (wax) accumulation.
4) For symptomatic control of seborrhea, antiseborrheic shampoos and emollients may be used every 2-7 days until the skin condition is improved (~2-3 weeks), then, bathing frequency should be decreased to every 1-2 weeks or as needed for maintenance. Antiseborrheic shampoos contain some combination of sulfur, salicylic acid, tar, benzoyl peroxide, and phytosphingosine and can be found over the counter in pet/feed stores or online. Malaseb shampoo is a good example.
5) Daily oral fatty acid supplementation may be helpful as an adjunct therapy (180mg EPA/10lbs). EPA is thought to be the most antiinflammatory of the essential omega-3 fatty acids. It's plentiful in fish oil supplements.
6) Vitamin A 8000-10,000 IU per 20lbs orally administered with a fatty meal every 24 hours. Improvement should be seen within 4-6 weeks.
7) For dogs with severe, greasy, malodorous, pruritic seborrhea, treatment with systemic corticosteroids may be helpful. Acitretin (a retinoid) may be helpful in some dogs. Calcitriol (vitamin D) may be helpful in some cases.
The prognosis is variable, depending on the severity of the seborrhea. This can be an incurable condition that requires lifelong therapy for control but if it has developed secondary to an allergic dermatitis or pyoderma (bacterial skin infection) it will abate when those skin disorders are treated successfully. Please respond with further questions or concerns if you wish.