Here is my setup.

Alpine Deck (AUX IN)
Power Inverter
Xbox1
PSP (To control the xbox via wireless network)
Wireless Router.

When I have the xbox power connected to the power inverter and the cord gets near the audio cable for the xbox I get a bunch of "NOISE" (or Interference) in my speakers? How do I stop this from happening?

 

Do not run RCA close to power wire.... or get some better quality RCA.

 

I'm fairly certain that all inverters give off a lot of noise and your audio cables are picking it up. Basically all you can do is keep them seperate and like he said ^^ try getting new SHIELDED cables.

 

Fixed the Issue: Ground Xbox Shielding.

Here is my setup:
Power Inverter
Alpine Deck with AUX
Xbox1 (Modded and running Xbox Media Center)
Sony PSP (Modded and running Xbox Media Center Remote Client) (video)
Wireless Router

Xbox's Network card is connect to the wireless Router. The PSP uses its wireless card to connect to the xbox (running XBMC) and control it remotely. I can access all mu audio files and play songs I want. Create playlists. All kinds of stuff. I would like to thank everyone here for their help and everyone at the xbox-scene.com forums for their information.

 

Just a quick observation too... the router that your using will be giving off lots of polling signals too... whether or not you can hear it will depend on your amplifiers. Like Class D's will pick up on the high frequency polling and it will sound like ticking noises.

My 2 cents.