Need major help hooking up a new receiver!!!(long)

All I can say is get a DVM and start checking continuity. The speakers should be around 8 ohms so if you set all the volume controls to max. You should read 8Ohms across the coils. Once you find them you could change one of the volume controls and see if the resistance changes that would tell you which leg of the speaker goes thru the controls. Without a wiring diagram you have a tough way to go......

Depending on first installer, I would guess one of two color codes used.
RED/Green = +/- for right speaker
White/Black = +/- for left speaker

OR
Red/Black = +/-
White/Green = +/-

Simple test if you do not have meters.
Get a good 9v battery,make sure volume control knobs are up to full volume, put red wire to +, and touch other wires to -, remove and touch again, as you do this and find the right pair of wires, one of the speakers will eventually make a popping sound. Once you hear the popping sound, you have found the + and - wires for that speaker. Next select other wires and continue untill you find all the speakers. I suggest getting a sharpie or other type of pen to write on the wire with so you don't forget.
Now you have all the speaker wires sorted out. From what you have described it's only 2 pairs of main speakers and a pair of surrounds we are dealing with.
Many receivers available have speakers A and B, which will make this easy, living room goes into A and kitchen into B. As long as system will let you play both at the same time, your set. You should make sure receiver volume is set possibly to around half way, then let room volume dictate how loud you want it in each area.
Good luck, and happy holidays.