Data acquisition wiring - How to deal with extreme noise?
There are two sources of noise, capacitive and inductive. 

Capacative noise comes from a voltage potential difference between two conductors.
In your case the power line would be one conductor and your device would be another, and can be modeled as a capacitor. 
To stop capacitive coupling, a faraday cage would be the ideal thing to stop any electric field that would produce a voltage on your sensors, cables and DAQ.

The ideal situation would look like the image below example c) The other problem is also grounding as the potential difference between your sensor and DAQ will most likely be at two different potentials. So try and make the whole system like example c) with shielding around the cable, sensor and DAQ. The shielding also needs to be continuous, so use shielded wire.


Source: http://www.7ms.com/enr/online/2010/02/notebook.shtml

Inductive coupling is harder to stop, it comes from magnetic fields and cannot be completely eliminated but can be reduced. Avoid loops as a magnetic field can create a voltage potential around the loop. Twisting wires also helps eliminate loops as it cancels out the magnetic field between loops. 



Source: https://www.researchgate.net/post/What_is_the_basic_idea_behind_the_twisted_pair_Why_are_the_two_wires_twisted_How_does_this_arrangement_compensate_undesirable_disturbances