I have a question about engine materials.

4340 steel (for crankshafts, pistons, rods, etc.) isn't extraordinarily strong. So why is it touted so?

Another one - why stainless steel instead of aluminum for exhausts? Al is lighter, more corrosion resistant, not that much more expensive, etc.

4340 is a high tensile steel, more info here http://www.interlloy.com.au/data_sheets/high_tensile_steels/4340.html

Steel in the piston, or did you meant piston pin? Steel is only in pistons for large diesels. For cars with high performance, metal matrix composite (silliconcarbide with aluminium matrix) is a good piston material.

Aluminium exhausts? Exhaust manifolds or what?
Stainless is corrosion resistant at high temperatures when aluminium would have melted. Stainless also conduct heat bad and that is a good thing for exhaust manifold material. The best material available today for exhaust manifolds is probably inconel, but the downside is the price.

OK, scratch the pistons par.

But for crankshafts, etc. There are a lot of materials that are stronger than 4340. First one that comes to mind is VascoMax's C-350 maraging steel. :)

Aluminum for the tubing between the cat and the muffler. Aluminum melts at roughly 620 C.