Some produce odor, others cause decay, which is where gum disease comes from. This is a direct result of plaque. If you want to eliminate odor, eliminate the disease and the plaque. The only way is daily brushing. Dogs' teeth are easier to brush than your own.
Dogs generally form most of their plaque on the outside of their teeth.
But occasionally they form plaque on inside surfaces as well. It's tough to brush inside there, so concentrate on doing the outside surfaces, and take your dog to the veterinarian periodically to clean the inside surfaces. Use in animals doesn't require a prescription. Chlorhexidines are polybiguanides, developed in World War II as anti-malarial drugs. In Europe, especially in France, they've been used as oral hygiene rinses for periodontal disease.