It’s simple. Three easy steps:
(1) Place plutonium rod in fridge (acquire from any passing terrorist).
(2) Weld fridge door shut.
(3) Call the cops to complain of a strange glow in the basement.
I believe they are honour-bound to repair any damage caused in removing said item from your basement …
Julie 
I think it’s obvious. They dug the foundations, put the fridge there and then built the house around it.
If it’s an old fridge, it’s probably metal, not plastic, right? Will the Sawzall cope with that? I still say cut it in two. And post pictures on the internet. Or video.
Even if you cut it half lenghtwise, you’re going to cut through tubing. Picture a lot of u-bends and you’ll see what I mean.
But, you might be safe if you cut off the front four inches. Might be.
(And yes, there are metal blades for reciprocal saws.)
Can you give the dimensions of the stripped down frige? Are there any turns in the stairs? What are your door widths? Most basement doors are 30 inches. (We have a “custom” one that is 26"
that’s a LONG story) I didn’t think even older refrigerators were more than 30" deep without the door.
Can you remove the door frame on the door at the top of the stairs?
Widening the door is technically still an option for you – just an arduous one. You’d need either skilled friends/relatives or a contractor crew to come in, tear part of your brick wall down, remove the steel door frame, and then rebuild your wall with a wider door.
…
Emilio, can you perhaps hire an AC/refrigeration professional to come in and perhaps thoroughly disassemble the fridge for you? I mean removing all the insulation, shelving, interior structural elements; and then safely disposing of any freon-carrying elements. The idea is to end up with a metal shell that can perhaps be sledgehammered into large pieces of scrap that will fit through your basement door.
IIRC the freon would mean death for Emilio.
I have two ideas though-
Idea The First
You don’t need to get the refrigerator out of the house, just out of the way. Rent a jackhammer. Make an appropriately large hole in the basement floor. Put the refrigerator in the hole. Fill the hole.
Idea The Second
You’ll need lasers for this. Fortunately, laser technology has become much more affordable in the past twenty years. You’ll need a targetting computer. Fortunately, pcs have become smaller, faster, and more powerful as well as cheaper in the past twenty years. You’ll need a mounting armature and computer controlled servos. I’m sure some of the other Dopers can help you find these cheaply online. Once you have these components, it should be a simple matter to build an oscillation overthruster and carry the fridge through not only the doorway, but the door itself.
Did you remove the refrigerator door?
I’m not convinced that the fridge actually has much freon left in in it – I tnink that’s one of the reasons that it doesn’t work. I’d rather not find out the hard way, though. It’s a very close fit through the door, perhaps less than 1/2 inch. Suppose I simply sliced 1 inch off of the fridges narrowest dimension (its depth) by cutting off the front of the unit. That shouldn’t expose anything too nasty, should it?
He’s got that covered:
I think that if you wait maybe 10^10^googleplex of years you will find that the fridge will be on the outside of the house at least once on account of quantum indeterminacy (the tunnel effect). Then get it out of your neighborhood before it goes back to your basement.
Actually, either burying it or slicing an inch off the front should work. But did they use asbestos?
I don’t think freon is toxic unless it’s exposed to an open flame. Wasn’t freon developed as a non-toxic replacement for ammonia?
Any way you could still use the fridge where it sits? Make it a big toolbox, oversize humidor, industrial paperweight… Maybe I’ve been watching too much Red Green, but this just screams opportunity.
The solution—dynamite!
I have spoken. 
I’d like to second Doc’s suggestion for a basement burial- think of the thrill you’ll be providing the lizards once they evolve and we’re long gone!
On A Serious Note
Whatever you decide to do, take proper safety precautions.
Wear work gloves.
Wear goggles.
A dust mask isn’t a bad idea either.
Have somebody else present(at a minimum safe distance) to aid you or call 911 in case of serious screw up.
Plastic and/or metal splinters in your hands and/or eyes are quite unpleasant.
Should you find yourself tempted to work without a net, just remember that dying in your basement while sawing a refrigerator in half is almost certain to win you a Darwin.
Get a sledgehammer and beat on the fridge until it’s 1/2-inch smaller. I don’t know, could be fun.
How about removing the floor above, and then use a wench to pull it up through the hole, put the floor back in place, then lower it onto the floor. Now it is out of the basement, but probably in your living room. Makes a great conversation piece.
Open fridge, find inside the number of the manf, call them & ask them what to do… If they don’t have a number anymore, call a local used appliance store & ask them what to do.
Tried acid yet?
I’ll second DocCathode’s comments. But I’d still cut up the thing. Remember, there’s nothing stopping you draining the freon first. Do consult your local Health & Safety people.
It should be possible to just slice off the top and bottom, then fold or bend the sides inwards. You may even find that it dismantles in this manner.
Is the manufacturer still extant? They may well be able to offer advice.
And afterwards, you can exploit the wench in other, more interesting ways!