Been reading a bit into the 4wd and AWD systems, Seems like the you need a "differential" (AWD) or a "Transfer box" (4WD).

If you want to put this inside an MR2 you'll need a gearbox which works with the Mid-engined layout, space to fit either a diff or transfer box and somewhere to fit a (couple of) axle(s) to power the front wheels.

If you move the gastank to the front that might resolve a bit of the space problem (and probably creates a few of its own).

On a side note, I actually found out that Toyota also made a Celica with four wheel steering, couldn't help to think that that's even more awesome! (A four wheel drive - all wheel steering - MR2 )