We have forced air heating system in our home. A couple of years ago we had the
Ducts cleaned because we were putting in an air conditioning system. After I couldn't stand the musty smell from coming from the vents. We had some of the duct work
In the basement replaced. We couldn't replace the ones going up through the walls.
The company installed the new duct work which had some kind of insulation inside to
Prevent moisture and mildew build up. They also used soft insulated ducts to connect
The main duct to the ducts leading up to the rooms. Ever since I had that work done
I have noticed a slight smoky odor in the rooms upstairs, and I have been waking up
With an irritated throat. Can you explain this?

Since you are there and we are here trying to smell something or provide an answer to you is just about impossible but you might check to be sure the A/C indoor coil is clean. You have to look at the underside of the coil to tell this so usuallyt a service person will have to do the inspection since most of the time the coil or other parts will have to be disassembled to see the coil. Next I would have a air quality check performed in your home. Hopefully that test will find a air quality problem and a cure.