So when I'm accelerating (harder) or sideways, my lights will flicker off then back on and the radio will usually die out and come back as well. I cleaned a few grounds and made sure they were tight.

Is there a main ground that grounds under the car? I'm not sure what this could be?

 

Clean a few more.

 

Oh man, I had the same problem with my 94 SC300. The weirdest thing fixed it though. Switching from halogen to HID kits for the low beam/fog lights. Ever since I made the switch it stopped doing it for some reason. Does your clock on your cluster reset as well? Mine was doing that everytime I'd take my key out of the ignition and anytime I pushed on the brake pedal and the brake lights would come on my cluster would flicker and the radio would shut off for just one second and then come back on its own. Was really weird, I never did actually figure out what was wrong with my car either lol.