Mark it: The biggest hurdle in hiding all those wires is to first get them untangled. Unplug the end of one cord and follow it to the source. Mark the name of the device on a bread clip, or simply write the name of the device on a piece of tape and wrap it around the cord near the plug. This step might not seem like a big deal, but doing it now will save you lots of hassle in the long run should you need to disconnect that particular cord.
Clip it: Half the battle in keeping your cords hidden is keeping them tidy and neatly organized. Gather in bundles and clip with with binder clips or zip ties to help control the chaos.
Wrap it: If it’s impossible to hide part of the cord, pick up a spiral wrap in the same color of your trim so it will easily blend in with the paint.