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Always pair a signal with its ground, and a supply wire with its return (typically ground again). Then the current returns in the same tightly confined bundle so that the net current is zero. This means no magnetic field coupling once outside the cable a short distance. Its all about magnetic field leaking out and leaking in and inducing voltages around the circuit. The twists mean that on average the fields cancel out, and tight twists are better for this. With a sensor whose supply wire is decoupled at each end of the cable you can treat the supply wire as a signal ground (its only ac that matters) - a three wire sensor can simply use a twisted triple of course. Adding shielding will protect against electric fields, but this is generally a smaller problem with low impedance circuits which are robust to stray capacitive coupling. Magnetic coupling will affect the voltage in a circuit of any impedance just the same, capacitive coupling affects higher impedances more. Magnetic coupling injects a direct error voltage, capacitive coupling injects an error current (which a shield can drain to ground, or a low impedance circuit converts to a miniscule voltage).

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Is there any way for me to stop the noise? No, I can't use ear plugs. I also have tinnitus, so that noise doesn't help. I can't use white noise all the time. It doesn't help.