Okay. They're really not sway bars, but anti-roll bars. Shocks/dampeners, to-ma-to/to-mah-to.
Everybody understands that these simple devices resist body roll from side to side, but that they have an exotic X-effect is rarely a subject.
The front bar, for instance, throws weight to the rear, and the rear bar throws weight to the front, in an X-pattern. Left front wheel to right rear wheel, etc.
If a front wheel is lifting right off the road in a tight, high-G corner, you "push" it back down by increasing the rear roll stiffness. And vice versa.
To be honest, I don't recall all the Audi tricks, but with that bunch anything was possible.
In my experience, most VW people use sway bars that are too heavy. Of course, a 22mm bar bent a certain way might act the same as a 19mm bar bent another way. And let's don't even get started on tuning with adjustable end links.