I think I'd address the issues with the run first of all, because you just never know when you might need it. A good run is an invaluable part of a set-up in my mind, because there will always be times you just can't let them out to free range - bad weather, predator issues, or you being gone for an extended period of time.
What did you use for the "flooring" of your run, or is just set up on the dirt it's built on? How's the drainage in that spot? Can you make the run bigger? If you use the "10 square feet per chicken in the run" formula you have twice the number of chickens in there than the space can handle. Can you use a deep litter for a surface, or maybe a deep layer of sand? Can you put up a run cover to keep it clean and dry? My chickens have been in the same run for almost 2 years. There is no mud, no odor, and they love it.
If you don't address the issue of the run's cleanliness, I'm afraid you are looking at more serious issues than just the smell and the appearance. If it looks unsightly and smells bad to you it is certainly affecting - or going to affect - your chickens' health. You can let them free range, but all that's doing is leaving the eyesore there and you haven't resolved anything. They will rip up lawns, flower beds, poop on lawn furniture (and barbeque grills, ask me how I know that!) and you can't guarantee that they will always stay in your yard and not go over to a neighbor's, nor can you guarantee their safety against predators.
I can't tell you what to do, of course, but I can tell you that if it were me I'd bite the bullet, tackle the issues in the run head on, and change it from an eyesore into a pleasant place for your chickens to be and a safe place to be able to enjoy them. Ignoring a problem and creating a potential new set of problems doesn't seem like it's in your best interests or the best interests of your chickens, your father, or your neighbors.