Strada cranks on track bike

Wait, why wouldn't you use the Pista cranks if you already got them? Wanna sell? Which vintage are we talking?

And to answer your question: probably yes according to this:

The forgings for the old 144mm BCD Strata and Pista arms were identical; only the final machining was different. You can use a Strata arm as a track crank but depending on your frame and bottom bracket you may have clearance problems with the inner chainring ledge and the chainstay. If that happens you can simply file off the ledge so it is flush with the rest of the arm. A true Pista arm will be counterbored so the stack bolt sits flush with the arm; without the counterbore the back of the bolt will rise about a millimeter above the arm surface. This is seldom a problem, and if it is it can be remedied by spacing the bottom bracket so the arm sits a millimeter further out.

http://www.bikeforums.net/bicycle-mechanics/614462-campagnolo-strada-144bcd-track-frame.html