"have an unusual (for us) problem with our 15-year-old Rheem gas furnace."

"but since the furnace had not been serviced since its installation"

Is this accurate??? I hope not! That's a problem by itself!!!

Thanks, bpChill -- you are correct, and it was good to have the furnace examined and cleaned up (the duct cleaning workers removed and cleaned the large fan box). However, the odor problem remained -- until I decided to spend most of the next day crawling around down there and checking everything out a lot closer. With the furnace running, I noticed that a large section of old fiberglass insulation was billowing out with hot air blowing from behind it. Upon close examination, I discovered that the original installers had left a 5" x 8" gap in the sheet metal case that comprises the blower box, and had apparently tried to cover it with foil-covered tape that had long since torn away. This was why the crawl space was always so warm when the furnace operated -- I was losing hot air into it!!!! I fastened down the sheet metal with screws, bought a small piece of sheet metal and screwed it down over the gap, installed new foil-covered (code) duct tape over all the gaps and wrapped the top of the furnace with a new bat of foil-covered fiberglass insulation. It was while doing this that I pushed up the wide, flexible ducting from the main house air intake where it entered the bottom of the furnace -- and saw a rat tail protruding from the narrow gap between the bottom of the sheet metal air intake box and the concrete pad on which the whole heater sat. The dead rat attached to the tail had apparently crawled in there, got stuck and died, perhaps a week ago. And jeez, did it stink!! Now the source of the odor was found; I disposed of the rat and scraped and vacuumed away the adherent material from it on the concrete, vacuumed up the remaining rat droppings on and around the pad and the old insulation, and pulled out and and disposed of the old, torn insulation. Within a few hours, the odor from the air intakes inside the house was gone. Success! The moral of the story is, if you smell what seems like a dead animal, it certainly IS a dead animal. One thing, though that concerns me about the furnace -- I've read that the electronic igniters (carbide or nitride)on these furnaces are supposed to last maybe 5 years. Mine is still going strong after 15!