Putting harsh drain chemicals or bleaches into a garborator is not a good idea because of all the metal, rubber and plastic parts. You might damage something. If it is really smelly it probably has some food stuff stuck in corners that just don't flush out.
Here is where enzyme cleaners come to the rescue. Any odour caused by organic decay can be cleaned up with enzyme cleaners because they are actually active bacteria that go in and actually digest the organic material, being totally harmless to all the mechanism and even useful to the a septic or sewer system downstream. They actually come out of the soil, and after going through your drains they will eventually return there.
For the first treatment I would suggest disconnecting the drain pipe and plug it up so that you can fill the garborator with warm water and enzymes. Leave it for at least 3 hours. They work well, but they are digesting and that takes time. After the first time, simply put a few ounces down the drain every few weeks to keep it in great shape.
They are often a bit difficult to locate although there exist specific formulas for drains, for septic systems, for algae infested ponds, even for cleaning aluminium siding. In the meantime you can often find one form of enzyme cleaner or another at pet stores as they are so effective on pet odours.