I have been looking into Litz wire for a DC-DC transformer I am building that will operate at 50-100 kHz or so, and it does seem that the skin effect is quite significant. Here is some theory:
According to my calculations, #1/0 cable at 350 CM/Amp is good for 300 amps, and has a DC resistance of 100 uOhms/foot. So 10 feet of cable would have a loss of 90 watts at 300 amps. However, the AC resistance at 20 kHz is 12.4 times that, so it may be very significant (1100 kW). However, that is just the carrier frequency and the effective waveform will usually be less than 200 Hz, at which the cable has about 1.24 times that at DC, and the losses will be 112 watts.
It might be good to use 10 parallel strands of #10 AWG wire which has a skin factor multiplier of 3.9 at 20 kHz, and negligible effect at the effective frequencies of 10-200 Hz. It would be interesting to run a temperature rise test on a #1-0 cable and a 10 strand bundle of #10 to see if there is any significant temperature difference.
This is actually AC resistance and not inductive reactance, so it is actual power and not VA.
The DC cables may benefit from having some inductance, which may help reduce the ripple on the DC bus link. I don't think the capacitor size is affected by the distance from the battery, and in fact may be reduced for a long DC run. The battery pack probably has a very high impedance at 10-20 kHz. And the controller may benefit by having a long run to the motor, as it may increase the load inductance and minimize high current spikes.
Skin effect may or may not apply to AC motor cables. But there are other effects that should be considered, so here is some information that may be useful:
The last reference is very detailed, but one important point is that the controller should be in close proximity to the motor. It also shows how the PWM and motor and cable characteristics can combine to cause high frequency ringing on PWM transitions and resultant high voltage spikes which can damage insulation as well as cause excessive capacitive currents which can reduce efficiency.