Pictures would be a lot easier to decipher in this case...
White and red wires: you're always going to get noise if your ground isn't connected well so make sure that is soldered on nicely. Then you've effectively just got a "hot" or live or signal wire. This is more or less linear and you can trace it forwards or backwards.
You can do work on a guitar while it's plugged into an amp and turned on,every safely. It might make some horrible loud noises if the amp is set too loud, but any electrical danger would be from a fault in the amp not your guitar. So get prodding with the thing plugged in and you'll soon find the issue!
For instance take a thin screwdriver or paperclip and hold it in your bare fingers so it's an extension of you, you big noisy antenna you. Now use that noisy poker to touch the output terminal on the jack socket. See how you can inject noise into the circuit?
Now move back along the signal wire and touch the volume potentiometer terminal where it's soldered. Same noise! Then you can switch over to the over terminal which is where the 3 pickup switches join on - you'll get noise, but only if the volume control is turned up! If you turn it down, it's stopping your finger-pokey noise from reaching the amp.
Use this method to trace connections until you have a clean line of signal from the pickup wire, through the switches and into the volume pot and then the jack.
Hint: the tone control is a parallel branch of this signal chain so you can sort of ignore it, unless your sound is all muffled constantly.
Bigger hint: all components should usually be grounded e.g. pickups, pots, bridge. Use a multimeter in continuity mode (beeps) to confirm this by checking against the guitar cable's sleeve/jack plug body.
Green wire: no idea, but I would expect there to be a bridge ground wire somewhere (unless those are active pickups). See if it has continuity with the bridge.