It does sound to me like you are describing a reverse sneeze.

Reverse sneezes have the same cause as a regular sneeze but are much more dramatic!

You should look around the home for allergens and eliminate them if you can. Carpet powders, cleaners and pollen are pretty mean culprits.

I found an informative article that might explain it for you better than I can.

Paroxysmal Respiration or "The Reverse Sneeze"

This is a condition very common in brachycephalic breeds and small dogs but is also seen in other breeds. Paroxysmal respiration, which is the medical term or what is commonly known as reverse sneezing is when a dog seems to be sneezing, but in reverse. The episode seems as if the dog is sucking in or honking and it lasts between a few seconds or a few minutes. To us, it appears that the dog is uncomfortable, but it is a common condition in small and brachycephalic breeds and the dogs return to their normal state when the episode is over. Some feel that massaging the neck and throat area help to stop an attack. In the "Textbook of Veterinary Internal Medicine" by Ettinger and Feldman, swallowing will stop reverse sneezing. According to their book, reverse sneezing can also be controlled by massaging the pharyngeal area or by briefly closing the dog's nostrils. Some people say that their dogs respond to rubbing of the upper neck area when experiencing an attack or episode. According to Dr. Mike Richards, DVM "Reverse sneezing is a problem of the pharyngeal region." Though there is no definite known cause of it, some have reported that it occurs with allergies, when dogs become overexcited or overheated, and some experts say that it is common when dogs suffer from tracheal collapse (another condition, common in small and brachycephalic breeds).

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I have found evidence that the massage technique mentioned above works well as does forcing the dog to swallow.

The odor could be a couple of things. The most likey cause is a bacterial or fungal skin infection. This can be a problem even if you see no redness or itching. You should see the vet to rule this out as a cause.

Another problem might be the dog's anal glands. Dogs have two glands at 10 and 2 like a clock beneath the tail. These glands secrete a smelly substance every time your dog poops. Sometimes these glands leak this foul substance and the smell is pretty bad once it's on the dog's skin. If you suspect this, you can use a baby wipe or vinegar wash to clean the skin on his bottom. Your vet can express the glands for you and hopefully take care of the smell.

If the odor is on the upper part of his body, I would feel led to think that he might be licking his anal glands and you're smelling the foul odor on his mouth.

Also, I would be concerned about the dog having yeast in the ears. This can cause an old dirty sock or locker room smell or it might even be a pungent, sweet smell.

If you have not tried it yet, you can wash the dog in a vinegar solution to combat the smell. Douches like women use work well for this because they have an applicator and you can spray the liquid onto the coat and reach hard to get to spots.

Dogs with chronic skin problems often have an underlying cause like allergies. If this is the case, you should discuss supportive therapy (antihistamines and a diet change) with your vet.

Let me know if you still have questions.