Looking for a way to get rid of cat's.

Today I called the Humane Society and told them about the cat problem in my yard.  The lady that answered the telephone told me they couldn't do anything, she said to call animal control.  I called Animal Control and was told I could rent a cage  at $25.00 a day and i would be required to deliver the cats.  I understood that for a price they would take the cat's I caught.   I may have misunderstood the part about paying them to take the cat's. 
I am about at wits ends with the cat's.  They have already cost me a lot of money and made me sick.  Every time I mow the lawn I get a face full of  cat poo dust.
If anyone has a legal sugestion please let me know.