Reddit mentions of Advantage II 6-Dose Large Cat Flea Prevention, Flea Prevention for Cats, Over 9 Pounds

I know of one solution to completely getting rid of them. I have 4 cats and even though they're indoor cats they had fleas. My wife bought "Bayer Advantage II Flea Control Treatment for Cats" from Amazon, we put it on the back of their necks, and it worked immediately getting the fleas off of them.

As far as getting rid of them (or any other similar insect, including bed bugs) in your house, diatomaceous earth is a great solution since it's a completely natural substance that contains no chemicals and isn't harmful to humans or animals. Diatomaceous earth has razor sharp edges at a microscopic level that gets into the exoskeletons of small insects like fleas and bed bugs which cuts them and dries them out... eventually killing them.

I restore furniture as a hobby and accidentally introduced bed bugs into my house. Pest control quoted us at $200 a room. I put the diatomaceous earth in one of these dusting bottles and coated my entire house. It made quite the mess from all the white powder but it worked immediately and I haven't had problems since... except occasionally cleaning up the excess dust that I sometimes find behind the furniture.

First, are you sure it's not fleas? Without a flea comb, I only find fleas on about 30% of cats that are infested. They tend to groom a lot of them off and make it difficult to find live ones. Feline hyperesthesia is very rare, so let's rule out the common things first.

Thyroid problem doesn't sound likely either because 15-20 pounds sounds fat to me. Most domestic cats (even large framed ones) shouldn't weight over 10-12 pounds. Most should weigh somewhere between 8-10. Unless you have seen weight loss in him, hyperthyroid is unlikely.

So to answer your question, I would get some good flea control and see if that helps. You can use Advantage II or a Seresto collar. Do not use anything bought at Wal-Mart.

I am guessing the cats are strays and not feral. Ferals are much more skittish and would not let you pet them freely, as you've mentioned.

1. Change the flea medication. There are a variety of them. Maybe try Advantage http://www.amazon.com/Bayer-Advantage-6-Month-Control-9-Pound/dp/B004QBDO0M/ref=sr_1_1?ie=UTF8&qid=1370895244&sr=8-1&keywords=advantage
   
   
2. I know the thought of giving them a bath is horrifying if they were strays. But this always helps. There are a lot of cat shampoos that can also help with fleas, so you don't have to use dish soap.
   Help with a bath:a) If their nails aren't clipped, clip them and you won't become a scratching post. b) Wear long sleeves and a scarf in case they do try to claw up your arms or neck c) don't dunk their faces in water, but have a bucket you can have them sit in since you don't have a tub and hold their front paws to help with the clawing. d) try a waterless shampoo. http://www.amazon.com/Veterinarians-Best-Clean-Waterless-Bath/dp/B0002AQN2M/ref=sr_1_2?s=pet-supplies&ie=UTF8&qid=1370895273&sr=1-2&keywords=cat+shampoo I haven't tried these, but people that have cats that don't like water seem to think fondly of it. If none of these things appeal to you, you can always take them to a groomer
   
   
3. Make sure you keep up with their grooming and medication application to ensure the fleas don't infest the home
   
   I hope some of this helps.
   

Advantage II

Bayer Advantage II for Large Cats Over 9 lbs, 6 Pack https://www.amazon.com/dp/B004QBDO0M/ref=cm_sw_r_cp_api_brpZxb3DY9V85