The 4051s are only useful, for your potentiometers. For leds, I'd use shift-registers. For buttons you could use input-shift-registers. Though there are better options. E.g. chips that can scan a matrix of buttons, or chips that send you an interrupt, if one of the buttons is pressed (so you don't have to constantly poll the button states.
As to the original question. You can connect the S1, S2, S3, and Z pins of multiple chips to the same pins on the Arduino. You need to use a different Arduino pin for each of the chips E pin.
You can then set the E pin of the chip you want to read to LOW. You then set the correct S1-3 pins to select which output/input of that chip you want to connect to. You then read the value from the Z pin.
I hope that makes sense. Otherwise, let me know.