interconnects vs speaker cables vs power cords - which make the biggest difference?

Me personally have found power cords will make the biggest improvement (they are the foundation for your entire system) followed by speaker cables and last interconnects. A lot will depend on the level of your system and what level of cables you're looking at.

Yes, it much depends upon the particular system, but in my system(s) I have consistently heard what several others have:

1)  Power Cords + conditioners make the greatest difference.
2)  Speaker Cables next (by a fair bit).
3)  Interconnects last (but not by that much).

I think that there is a case to be made for "mixing and matching" different brands to balance out at the right sound for you, just like one might in tube rolling an amp.  That said, I have virtually all one brand in my system currently...  Different systems call for different solutions.

IMO. Speaker cable followed by power cable, interconnects. Your results may vary.

OP,  Lots of good feedback here, based on my experience and feedback from cable manufacturers, 

1) Power cords
2) Speaker Cables
3) IC's

Equally important. You cannot get any sound unless you have connected power and speakers and source to amp.