If all you want to do is change the rear differential oil you could leave the drain plug where it is and suck the old oil out. The tool for doing this used to be some where in the $13-$20 range. See picture.
You can get one at the local parts store.
Another option is to leave the plug in and loosen or remove the differential cover, drain, and reinstall it with a gasket or sealant.
Go to the junk yard and get another differential cover with a decent plug (remove the plug at the junk yard to be sure it will come out).
Otherwise you will have to do what ever is necessary to get some sort of Eze-out out into the plug to turn it out. Usually requires the proper size drill, Eze-out and sometime a tap to restore the threads.
They may have a newer type of EZE-OUT now for stripped internal allen/hex type slots that you will not have to do any drilling to use but I have not seen them or have any experience with them.
Another messy option would be to drill, tap, and thread the existing plug for a smaller american pipe plug. When the drill enters the differential the draining oil will was out the chips. When you use the tap put thick grease on in the tap flutes (grooves) and the grease will trap the cuttings as you thread the tap in.
Motor Drain Oil Fluid Suction Siphon Pump

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84 300D, 82 Volvo 244Gl Diesel

I think Diesel911 has you covered with correct options. You can remove cover and let that god-awful smelling mess drain and reinstall cover. Should be fine that way, or as stated go find a cover at a salvage yard.
Man that stuff always smells nasty!

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Jimmy L.
'05 Acura TL 6MT
2001 ML430 My Spare

Gone:
'95 E300 188K "Batmobile" Texas Unfriendly Black
'85 300TD 235K "The Wagon" Texas Friendly White
'80 240D 154K "China" Scar engine installed
'81 300TD 240K "Smash"
'80 240D 230K "The Squash"
'81 240D 293K"Scar" Rear ended harder than Elton John

You probably should remove the cover to see if any metal particles from the old plug got loose in there

BTW, one should always remove the fill plug first, before the drain plug just in case it (the fill plug) is stuck.
Anyhow you will need to either find a junkyard w/ a 126 chassis to snag a p;lug from or buy one from the dealer, it can't be THAT expensive.

I haven't seen those plugs sold as aftermarket or replacement items. When you remove the cover let it drain a day (or longer) to get all the stinky stuff out. Some purists have said they flush the old goop out by running synthetic 75W90 in there and replacing it after a few months with more fresh lube.
I recommend Amsoil synthetic for its longevity.
The level isn't that critical. I've never measured it out, if the car is level you just fill it until it spills out of the fill opening. I usually have access to a lift but if it was jacked up I'd still fill it by eyeball, let the car down with the fill plug out to let it drain a bit then jack it back up and replace the plug.
Good thing you don't have a 124 chassis, the rear cover is sandwiched against a lower cross member and its a big job to get to the cover.

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'95 E320 Wagon my favorite road car. '99 E300D wolf in sheeps body, '87 300D Sportline suspension, '79 300TD w/ 617.952 engine at 367,750 and counting!

I'd remove the cover, clean it up and torch that plug out. I can't imagin the dealer can't get it the next day for a few bucks.

I used Mobil 1 75w90, but I use Mobil synthetic fluids throughout the whole car. Amsoild or Redline work.

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2016 Corvette Stingray 2LT
1969 280SE
2023 Ram 1500
2007 Tiara 3200

I believe he said the wrench area of the plug was stripped out; no tourch will help that unless you mean burn the plug out with a cutting tourch. If that is the case he possibly would need a tap to restor the threads.

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84 300D, 82 Volvo 244Gl Diesel

No its a big plug, you can do many things to get it out. Torching the cover will expand it and make the plug very easy to extract. You can either tap it with a left hand thread bolt, or use one of those screw extracters.

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2016 Corvette Stingray 2LT
1969 280SE
2023 Ram 1500
2007 Tiara 3200

Read last three previous posts.......

You only want to "heat it up," to make removing it easier.

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'06 E320 CDI
'17 Corvette Stingray Vert

My personal choice of all the posts I have seen so far and the fact that the differential oil seldom needs to be changed would be to suck out the old oil through the filler hole.
If something else came up later like changing an Axle I would deal with the stuck plug.

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84 300D, 82 Volvo 244Gl Diesel

This is what I remember reading from the start of the thread:
"And then I go and look at the drain plug and it seems to be smashed/ chewed up, and just not in a good mood. Someone, before me, didn't treat her nicely".
This gave me the impression that there is nothing left to get a wrench on to turn the plug out. To me this means heating the plug will do you no good if there is nothing left to turn it.

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84 300D, 82 Volvo 244Gl Diesel