What is this smelly , nasty, chalky stuff that comes out of my healed piercing?

It is seburn. Seburn is produced by your sebaceous glands & ducts that are located throughout your skin in the skin(including the skin inside of piercings). These glands produce oils and fats and generally open into the hair follicles and give off seburn. Seburn then seeps into the hair follicle and works it's way to the surface where it spreads into a thin film. Seburn main function is to lubricate the hairshaft and to produce a film that helps prevent excessive evaporations and absorption of water and excess heat loss. It helps to water proof the skin. When this fatty oil blocks the skin open, it forms a blackhead. Seburn also helps in maintaining the normal acidity or PH of the skin and keeps the skin soft and pliant.

Since the exit of a piercing is usually blocked by the jewelry, Seburn will collect inside the piercing. This is more common in areas of the body where there is a high concentration of Oil Glands like the forehead, face, neck, and chest. In fact it coats you entire body except for areas that you need more traction like the hands and feet. It's your bodies natural water proofing, insolation and lubricant. It tends to be even more common in slow healing piercings like the nipple or piercings that are being or have been stretched like large lobe piercings. The more skin the more ducts the more seburn.

Since this is a natural product of healthy skin it poses little or no health risk. The odor can be over powering though and it can be removed by cleaning the jewelry when you take a shower or bath. Also since organic jewelry will tend to absorb the oil it can reduce the smell unlike acrylic that tends to add to the collection.