New strange smell.

question edited for clarity and typos.

Strangely, they have a history of it!!

https://www.google.com/search?q=Frigidaire+Refrigerator+Model+FFTR1814QB4A.+Terrible+odor+in+fridge+and+freezer

..

sulpher in water, or leak of coolant

PUT A BOX OF BAKING SODA IN REFRIGE AND 1 INTO FREEZER ALSO. BUT TAKE EVERYTHING OUT, MAKE SURE NOTHING SPILLED AND IS UNDER A DRAW ROTTING. IF ALL IS CLEAN INSIDE, PULL OUT REFRIDGE IN BOTTOM BACK IS AN EVAPORATOR PAN FOR CONDENSATION, SOMETIMES SOMETHING CRAWLS UP INSIDE GETS TRAPPED AND DIES.
YUCKY BUT VERY REAL

There is no danger if there is a leak, but the refrigerator will quit cooling. I suspect perhaps you have a dead something underneath or behind the refrigerator. I hope this helps... but I also suspect you have cleared the problem by now.

If new plumbing, system is flushing and may cause a bad taste or odd color.Has a food item spoiled?
Make sure that strong smelling food (for example, fish) is wrapped so that it
is airtight.
Clean out your freezer periodically and throw away any spoiled or suspect food. Place foods in airtight containers to prevent the transfer of odors.And also Flush out water hose from tap end to freezer with warm water And also clean fridge with wet cloth (with soap solution). And then clean with dry cloth. .Keep fridge door open after cleaning all compartments for 4hrs minimum, as fresh air could wipe out any bad odor in fridge. And then start using fridge. Hope, it's helpful.

Change the water filters in the line. They should be changed yearly. You can get parts, manuals, and more at repairclinic.com

buy a new freezer and never go near it with a screwdriver try unplugging it to remove ice

Sometimes the smell comes from something in the freezer or even the refrigeratior and makes the ice taste funny. My suggestion is to clean out the freezer compartment of anything frozen that has been there a while and may have freezer burn. That may be the funny smell you are experiencing.
Hope this will help you.

I picked up on something you wrote within your problem description. "got the thermostat replaced under warranty" & "that worked for a while ". back in Aug of 2002. It's August of 2008 and your thermostat may have failed again. 6 years later... not so unusual. Anyway, since your fridge has a bottom freezer, there must be a pass thru between the freezer and the fridge compartment in an area you haven't examined yet. The fridge gets cold air delivered from the freezer to keep it cold thru this pass thru and many fridges have an adjustable flap that allows you to limit that cold air flow. Time permitting, can you do a more thorough examination of the fridge area ( side walls near crisper drawers perhaps?) or better than that, remove the drawers and look for that air duct pass thru. Once located, if it does not have an adjustable damper, try a little duct tape to limit the amount of cold air from migrating into the fridge compartment. Other options: Can you contact Amana customer support directly and get their support? That particular model has been discontinued by Amana but they should be able to support it. Not sure I added anything to what you already know. Gave it a shot thou...

I may have found the problem. I pulled out the Fridge again. The odor was in the water pan.

What I found was that the cooling grills in the front was caked with dust. I vacumed this area but it was not until I got down with a flash light and saw this issue. I took a small duster that uses static to pull the dust out. There was a lot. I will see if the smell starts up again.