I have been researching both municipal and county laws regarding the issue. Apparently I cannot even discharge a pellet gun within Overland's city limits. So the shooting of anykind idea is out. I also imagine the paintball idea may be similar, and even if it isn't, if someone saw me shoot a cat with a paintball gun, I am sure they would call the police for animal cruelty. So, again, shooting is out.
I also have looked up scheduling for Overland's city council meeting, which I will attend as soon as there is another meeting. The woman that babysits my daughter will also be attending as well as a few of the people who signed her petition. Hopefully this can spur some sort of action to be taken.
Muddy, I have done quite a few web searches over the last few months regarding the matter. I posted this thread hoping that someone may have an idea that I have not come across on your run of the mill web search. But, pertaining to some of the information in your search link: I keep my property as clean as possible and have made sure there are no spaces the animals can use for shelter. Unfortunately, one of my neighbors is not quite so neat and I am certain his backyard is a great place for at least a few of them to hide. I could use some of the sprays that are listed, however, almost biweekly reapplication is required in most cases. A single bottle of the stuff costs at least $20.00 in my neck of the woods at my local hardware store. That's going get pricey awfully fast and is not even completely guaranteed to work.
Fluke, I am not certain if anyone in the vicinity is feeding the cats. If they were, I am not even sure they would admit it for fear of recourse from the city code enforcer since he left all of those notices on everyone's doors. One thing about this area is there are many people around here with bird feeders. Easy predation of the birds may be keeping them in the area. I will try to convince my wife and neighbors to try an experiment and remove the feeders for a short period to see if it helps alleviate the problem.
I think the safest, most practical, and cheapest course of action for me to take will involve trapping the animals myself with the cooperation of the local animal control department. I will call them this afternoon to see if there is anyway something similar to what Grimlin described can be set up. I will also try to call Overland's animal control/rabies/code enforcer to bother him again about setting up additional traps. If I don't get anywhere with either of these phone calls, I will just have to call as many animal shelters, vets offices, etc., as I can to see if they are taking the cats. If they aren't, I am not really sure what I am going to do with the animals. Some of them I have seen are kind of sickly looking while others are a bit on the aggressive side. So I am not to sure if an animal rescue agency of some sort would take the animals, but I suppose that will be another avenue to look into.