Is there any way to calculate the voltage & current rating on an unmarked component?
Physical size will give you a good idea of resistor power capability. 

Transistors and diodes can be tested to breakdown without damage in some cases using a curve tracer or equivalent experimental techniques, but unprotected MOSFET gates can be damaged, and possibly bipolar transistors as well. 

There is no sure way to determine ceramic capacitor voltage ratings, and size may be misleading since older parts were much larger for the same ratings. You can plot capacitance vs. bias voltage.

You can measure inductor saturation current and estimate current rating from the size and resistance. Measuring core losses at various frequencies takes more equipment. 

There is a little open board, sort-of open source AVR-based tester that will identify various active and passive parts and give you values. Search for GM328, should be less than $10. Image from ali. 



I can't imagine any of this being of much value though, valuable parts will likely have markings and if you have enough cheap parts to be valuable the packaging will have markings.