E-153 Transmission Conversion
This is the alltrac gearbox.
If you look at the pic this is what u have to do:

-remove the green thing which is the bracket for the gear shifter cables from the alltrac tranny and put it onto the mr2 one.
-unbolt the bolts in the red and yellow square and remove the entire yellow/red/purple sections on the alltrac tranny. When u remove the red bit the shift linkage comes out of the gb. For it to come out you need to remove the bolts in the pink box.

-u need to remove the red bit in the mr2 tranny but this has nothing coming out of it. The shifter stuff comes out of the opposite end. To get this out u need to cut of the shifter stuff and then u can pull it out. Replace this all with the alltrac stuff and cover the whole at the opposite side where the alltrac linkage came out of (use a coin or something).

- u need to make holes for the bolts in the yellow square to go into. The space is there, just
make a hole and tread it.
As for the axles.....
After searching everywhere on the internet and asking alot of people questions of which axles to use with the 3sgte swap with a E-153 MR2 turbo/Solara tranny...I was finally able to get the right information and this is how you do it:
1)Look on Car-part.com or at junk yards for these parts:
a)1991-95 MR2 turbo intermediate axle w/ carrier bearing or purchase the entire passenger side axle if you want to be sure to get all the parts and driver side axle(you will need the inner shaft which inserts into the transmission)
b)1990-93 All-trac front axles for driver and passenger sides( they are actually identical in everyway)...make sure you find out if your car has ABS and order the axles pertaining to your car if it equipped with ABS or not. I am not sure if there is a difference but it would be a waste of time and money if it was.
2)The driver side all-trac axle was simple. There are 6 allen wrench bolts which hold together the inner shaft to the axle shaft on the MR2 turbo driver side axle. Place the piece with those 6 bolts into a big vice and get a allen wrench and a long pipe to get some leverage on those bolts.
3)After you have taken out all the 6 bolts, loosen the vice and seperate the two pieces. You should now have the MR2 turbo driver side axle in 2 pieces.
4)Place the Driver side MR2 turbo axle (HUB end) on the side and place the all-trac axle (HUB end) lining up the 6 bolts onto the MR2 turbo inner shaft end. Torque down those bolts.
5)At this point you should have the hub disconnected from the steering and the strut. Place the inner shaft into the transmission and shake it and turn it until you feel it pop into place. Then lift the hub and insert the shaft into the hub. BTW...All-tracs,GTs,and GT-S' all have the same hubs so the all-trac axle should fit perfectly with no problem. Torque everything down.
6)Now for the passenger side which is a little bit more work but basically the same idea as in instructions #2-#4. You dont need to do any work to the intermediate/center shaft. You will see the same 6 allen wrench bolts and you will swap the MR2 turbo outer with the all-trac outer.
7)Installing the passenger side is easier if you have someone help you hold the outside end while you push,turn and wiggle the shaft into the transmission.
8)when you feel the shaft pop into place line up the carrier bearing to the engine block and place 2 bolts. (It is obvious where you will see the holes line up for the bolts)
9)Make sure you install the support bar that bolts to the carrier bearing and the engine block for added support.You may have to pick up that stay/support bar seperately from the dealer or if you are lucky it will come with the MR2 turbo axles.
10)Same thing before with reassembling the hub end and voila! You have a working axle setup with a MR2 turbo/Solara tranny.

I just did the conversion ur talking about today. This is how u do it:

You cut the MR2 selector shaft with a hacksaw or grinder just infront of where it coems out of the gearbox, only way to pull it out. Then you undo both top plugs, filler and vent, and undo the front selector cover. then pull the MR2 selector shaft out. Use the GT4/Celica selector cover and push the shaft in, and bolt it up. You will need to use a clearance drill and tap on the castings on the top of the box to bolt the selectors down casue its not drilled, thats quite simple, just dont go too deep. Then tap it, i think its M10x1.25. Just get a tap same as the bolt out of the FWD box that holds the selector arm to the casing.

Make a welsh plug for the front of the selector housing where the mr2 shaft came out of and glue it in.

Presto! Your done. Can do it in an hour or 2.
Here's another explanation.....
Thank you Sepand Navidi for this write up