Speaking as an ex RAF Flt Eng who flew the Hercules for many years I have never seen, nor heard, of any requirement to use asymmetric thrust for anything other than a 3-engine T/O (ferry flight). The odd exception is 2-engines out or if within a tactical take-off situation. For the purists, there are also some situations whereby the use of asymmetrical thrust might be useful i.e. flying control restrictions. On a day to day basis of normal operations I cannot think of any reason to go "outside of the box" of SOPs.
As previous posters have said, the take-off roll (and subsequent engine failure prior to V1) does not require abnormal NWS inputs. The NWS is obviously utilised during the initial acceleration and prior to rudder effectiveness. If an engine fails prior to V1; immediately close the throttles and commence maximum braking. At Flt Idle, the handling pilot will order "Shut Down No.x Engine". The handling pilot will then select Ground Idle and apply maximum reverse thrust on the remaining symmetrical engines. The handling pilot will then transfer his hand to the NWS tiller whilst the non handling pilot takes the control wheel.
The use of NWS at higher speeds is not recommended.