We moved to a house built in 1965 from a 1915 house with a dirt basement. Against what I anticipated, the 1965 house was much dustier. It was like felt on top of everything. I cleaned and cleaned and it did become less dusty over time. We then found out a cat lady with over 2 dozen cats lived in the house in the past. We then had to get our furnace replaced and I was able to look down some of the duct work, the dirt and debris was 3-5 inches deep. Additionally, the basement ducts were entirely plugged with debris including dirt, seeds, ants, toys, etc. I had already removed what I could from those. We had our ducts cleaned last year, and the dust in the house is greatly reduced. Also have lost the runny nose I got after moving here. There are duct cleaning con artists out there, but ours did a good job.
Equipment used to clean ducts varies widely. The cheaper the equipment used the more you are just wasting money. This is why it's typically not worth doing. In some situations it may be beneficial, but only after determining and investigating the duct system. This should be done by a licensed HVAC contractor and not a duct cleaner that typically do not hold and HVAC license. (Duct cleaners aren't required to be licensed in HVAC in many areas.)
Your HVAC unit and air ducts deliver heated or cooled air throughout your home year-in and year-out. The air your HVAC unit produces travels through your ductwork and heats or cools your home via the air vents in each room. The dust and other particles in your home’s air are known as particulate matter, which the EPA defines as "a complex mixture of extremely small particles and liquid droplets." The EPA also notes that "particle pollution is made up of a number of components, including acids (such as nitrates and sulfates), organic chemicals, metals, and soil or dust particles." Having clean air ducts means fewer of these particles moving through your home. If you remove your furnace filter and hold it up to the light, you can probably see several hundred of these minuscule particles floating in the air. 
The short answer is yes, duct cleaning, done right by a reputable company will help with the smell. It is likely though the smell is coming from another source, ie the crawl space. It could also be that another rodent is dead in the duct work. A visual inspection would be in order to check for any breach in the duct system. A duct pressure test would be able to tell you how much air is leaking from the system over all. A hole large enough for an animal to enter would loses a great deal of air, over 300 CFM. It would be worth looking into having this test done and it should cost around $200. Cleaning the air handler and evaporator coil will greatly improve the performance of the air conditioner. Dirt and dust on the evaporator acts as insulation and reduces the amount of cooling done be the coil. Any quality duct cleaning should include cleaning the air handler and coil, and the tech should allow you to watch him perform the work as it is done.
Metal is way better than flex duct or ductboard. It gets better airflow, holds up to critters and duct cleaners. I know of no hvac company here that cleans ductwork. (there probably is one somewhere) The mfg's of duct cleaning equipment keep trying to sell us hvac people on their benefits and profit potential but most all hvac people know that unless you have metal ductwork you are NOT doing the customer any favors.
The amount of time it takes to clean a residential HVAC system depends on many variables such as the size of the home, the number of systems, the extent of the contamination and the number of HVAC cleaners performing the job. Ask at least two contractors to inspect your system and give you a time estimate for your particular system. This will give you a general idea of how long the job should take as well as an idea of how thoroughly the contractor plans to do the job.

I to had an odd layer of white'ish dust building up especially during seasonal periods when the HVAC ran a a lot. I carefully swept up the fine dust into a small pile and had it analyzed. Turns out it was very fine fiberglass powder dust. It turns out it is the insulation form the attic! (My attic has blown in insulation). Turns out if you (I) had small gaps around my HVAC registers in the ceiling whee the airs blows into the room. What occurred in my case was that the exiting air at that seam creates a vacuum effect at the grate vent cover and draws and then blows fine insulation dust from the attic into the house. Removing each register grate and sealing each tin outlet gap with calking between the dry wall ceiling and tin fixed the issue. A couple were so bad with bowed gaps I had to screw down the bowed tin to the attaching stud better. Checking the very same glass top desk that catches and shows any dust accumulation now shows only very small amounts of normal house dust build up over several weeks. A big, big improvement. You might have a look by simply removing a couple vent covers yourself.
Is duct cleaning worth it? There is not a yes or no answer that suits everyone. On an Air Force base, the system was not air tight and there was leakage around the filters. The system got dirty. A professional company was called out. The Duct was big enough that a technician could go inside the metal duct and clean it. There was a new Air Handler installed and things were sealed up better. in this case it was worth it.
Most people are now aware that indoor air pollution is an issue of growing concern and increased visibility. Many companies are marketing products and services intended to improve the quality of your indoor air. You have probably seen an advertisement, received a coupon in the mail, or been approached directly by a company offering to clean your air ducts as a means of improving your home's indoor air quality. These services typically — but not always — range in cost from $450 to $1,000 per heating and cooling system, depending on:
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