Are there 4 position switches that control power to a circuit and provide state?
You can use a DP4T (dual-pole, quadruple-throw) slide switch, like this one: http://www.digikey.com/product-detail/en/SS-24E06-TG%205%20(P)/CKN10394-ND/2747191
Since the two sides are independent, you can use one of them for power and the other for the signal to your Arduino.

On the power side, you'd wire the common (middle terminal) of the switch to the Vcc of the Arduino and three of the four other terminals to the power supply.

On the signal side, you'd wire the common to ground and the other terminals to inputs of the Arduino. (Don't forget pull-up resistors.)

The switch I linked to has the nice feature that it is make-before-break (MBB), according to the Digi-Key listing, so the Arduino won't lose power while the switch is being slid. If you actually have three separate power supplies, you don't want this, as two of the supplies will be briefly shorted together when you slide the switch. Instead, use a break-before-make (BBM) switch, and add a capacitor large enough to power the Arduino for the few milliseconds while the switch is sliding.