well first off your sony amp has an alpine logo on it..... With the amp in there it should be pretty easy just depends on how much time you want to spend on it. For best sound your best option would be to run 2 sets of rca's from the deck to the amp. At the moment it must be using a Line out converter which will work but is not as clean of a signal. If you do that, all you should need to wire up on the deck would be the power wires and the remote turn on for the amp(yellow,black, red(orange wire if you deck has one)) and then you can simply insulate all the speaker wires on the deck(grey pair, green pair, purple pair and white pair).
If you do not want to run the rca's and remote turn on then go ahead and wire up the colored pairs of speaker wires to their matching pair in the factory hrns.
They probably removed the stock x-over/amp that was below the radio giving you the extra harns's. Don't let them confuse you as you should only be able to plug in the ones you need into their matching pairs.