They have a fluffy undercoat and a very stiff outer coat, which is waxy not oily.
If a Lab is smelly, it's probably because of food allergies. Usually they also are itchy, have dandruff, and a dark smelly ear discharge.
The cure is to put them on a good dog food that doesn't contain corn, and if that doesn't work then go to a grain-free food.
My Chocolate Lab, now 12, had smelly ears - we put her on AvoDerm which is for dogs with skin conditions, then on Wilderness and now she and my other two dogs are all on Blue Buffalo Freedom, which is grain-free but lower protein than the Wilderness. Her ears are perfect.
Many thanks to all for your replies. I need a dog / companion / friend!