1) If the non-audio electronics are plugged into a separate power strip, but are not operational (i.e. off), will they still cause interference and degrade the sound quality of my system?
2) If I use an extension cord running from a different duplex outlet to power my non-audio electronics, will this resolve the issue?
The answers are yes, and possibly.
Have you evaluated all the elements that are on the same circuit as the outlet you are using? It's easy to test. Just turn of the breaker switch that controls that outlet and see how many other outlets and light switches are affected. If other outlets are affected whatever is plugged into those outlets could cause noise pollution on the circuit. Ditto if there are dimmer or high noise light switches controlled by this circuit.
If you do the extension cord tweak, and it seems to be your best option as far as I can tell based on your budget, you need to make sure you select an outlet that is as isolated as possible. In my scenario I have my gear plugged into two outlets on the same circuit, none of which has any light switches controlled by it and the unused outlets on the circuit have nothing plugged into them.