what's the easiest way to detect how *long* a path of circuit is?
There is no easy way to do this. All the ways are hard.
Basically, if I wanted to put wire on, say, Jenga blocks, and then be able to tell how many jenga blocks are ontop of eachother, what would be a solution?
There would be no solution that you could do with an Arduino.
The best way is with time domain reflectometry:- http://en.wikipedia.org/wiki/Time-domain_reflectometry
But not with a Uno. you can't.