This is the best way to weld diff's up, you'll want to use a 220 mig machine and .035 or .045 solid wire. Stick and dual sheild mig welding makes too much of a mess and you'll never get all the slag out, and it always seems to go straight into your bearings and launch the diff. Make sure to remove the bearings and ring gear.
First off once you've got it out you need to get it super clean, by using alcohol or brake cleaner and a rag. Any oil left over will cause perocity in your weld and make it weak.
If you have some, spray anti spatter all over the inside and outside of the housing, this will help with cleanup once its welded.
Make two plates using at least 1/4" steel to fit between the side gears.
Make sure your plates sit flat on the bottom shaft and don't wiggle around, then tack them into place. set your temp high enough to burn deep into the gears, the teeth should actually melt into your weld. Make sure to fill the area where the gears mesh together with a good solid weld.
If you feel you need a second pass weld the same way but just above the first weld so that it rolls smooth into the first one and makes the tops of the gears disappear. Now you have to clean up all the little bb's, use a pneumatic scaling hammer and a thin chisel, but you can use just a thin chisel it'll just take longer. make sure to get all the ones you can see, and for the ones close to the weld
that won't chip off you can hit them with a grinder or dremel tool. Then flush the whole part in degreaser and clean it the best you can. Drive the frashly welded gear 5 miles and drain the diff fluid and refill, drain and fill again after 100 miles or a couple wheeling trips. installing a magnetic drain plug would help as well.
I only recommend doing this to a front diff, and using manual hubs with it.
With the front welded with manual hubs, you can go anywhere. just make sure you unlock the hubs when turning/not crawling out of somewhere.
I did my front on our 1st montero and it was unstoppable. You just give up the normal 4x4 driving mode.
This is a Montero/Pajero/Delica open front diff and this is where you would weld:
