Why don't torsen diff's require gear oil? Hasn't there got to be very high pressure and frictional forces between the gears when the diff is in action?

 

Exactly that. They use gears to operate just as the stock open differential (and entire transmission) does. dino 10w-30, Torco MTF, or Torco RTF for high power or race transmissions. Honda MTF if its just an economy car that doesn't see high RPM (which an LSD is just working against the whole purpose of hypermiling).

 

That's fine, but unlike in an open-diff, the driveshafts are interconnected to resist differentiation in the proportion that torque is applied to the diff housing.

 

Yes, and thats what a good MTF is for. Even a poor MTF like Honda is good enough for daily use. There isn't so much pressure that it squishes all the oil out so the gears are dry, and there's not enough friction (thanks to the oil) that heat is an issue. Remember helical LSD's are still open lubricant, unlike a viscous LSD where heating the internal fluid of the diff is a problem.