I can't find any threads on this; but I see more and more examples of steel and maybe titanium(?) frame builders doing this. Good idea?

Can they add a lot of stiffness to a frame without adding weight?

Is there any directionality to the added stiffness?

Which are the most important tubes to do this to- if you were going to do it?

Picture? I know of tubes with internal ribs...

I would think the chainstays , mainly?

Twisting forces in mechanical structures are called "Torsion".

there is no benefit to the "twisted" tubes, and in fact a round tube of similar cross-section and wall thickness is stronger and stiffer. This is sophomore engineering. These tubes are a marketing gimmick, pure and simple.

Tubing with a square cross-section (and a twist in the case of Lynskey's Ti Helix OS) provides significantly more torsional stiffness than round tubing of the same dimension (e.g. 31.7mm x 31.7mm x 1.0mm wall thickess square vs. 31.7mm O.D. round x 1.0mm wall thickness) at only a slight increase in weight. IOW, round has about 60% of the torsional stiffness of square, and weighs about 20% less than square in round numbers. It's a legitimate trade-off in applications where torsional stiffness is important.

https://mnhpva.org/tech/frame_tubes.html

Same term influences both bending and torsional stiffness, back in the day we called it moment of inertia, but a lot of people call it second moment of area.

you're misreading your data. It's hard to state without making some nit-pickable error, but you have to use more material in a square to get more stiffness. Granted, if all you have is a limited amount of space (and that space is square) and are willing to go with more weight, you can get a stiffer tube. The twisted tubes really give up the advantage of the square because their outer dimension is more like a round tube.

The other issue with square corners is the potential for cracking, which has been reported on some frames. Additionally, for thin-wall tubes, the beer can bending modes may significantly reduce stiffness.