The constant moisture on the face can cause a red yeast infection....hence the stains and the odor you describe. Typically antibiotics are used to clear up the infection.
Next on the list would be an attempt to determine why he has excessive tearing. Clogged tear ducts, a slightly turned in eyelid, food allergies can all be a cause.
Ask the Veterinarian: Puppy's eyes, small breed dogs, large breed dogs