With this kind of an issue you may need to abandon the ductwork due to the 4 letter word...mold.
Anyone who tells you it can be cleaned is selling you something...a wet towel.
Ductwork needs to be cut open and scrubed down to remove mold entirely...the air nozels and hoses and wands are a minimal effort at best.
Get a professional heat company with a good reputation to give you an idea of what you should do next.
This could be a serious problem.