Center diff lock makes the speed of the front and rear drive shaft the same.
VSC is Vehicle Stability Control. This uses inputs from the steering wheel and an accelerometer to detect if you are skidding. It will use brakes and cut engine power to try to fix this.
Auto LSD uses the brakes to try to keep both wheels on an axle going the same speed.
Without the CDL and LSD, all the power will try to just find the path of least resistance. You could be sitting there spinning the one wheel with the least amount of traction. (this isn't exactly true because we have a Torsen center diff which works a little differently)
You don't want to drive on the street with the CDL locked. Both axles will try to spin the same speed, but when you turn you need one axle to go faster than the other. There will be binding and tire scuffing and eventually you could break something. Only use the CDL when there will be some slippage, such as in snow or mud or offroad.
VSC will get very confused very quicky offroad and will think you are skidding all over the place. It will rob you of power and you will get stuck, so turn it off before going offroad. (locking the CDL turns this off)