Magnetorheological-damper-based steering apparatus and methods for reducing steering wheel jerk resulting from off-road wheel impact are described. An example steering damper apparatus includes a magnetorheological (MR) rotary damper to be operatively coupled to a steering column shaft. The example steering damper apparatus further includes a sensor to detect an angular velocity associated with the steering column shaft. The example steering damper apparatus further includes a controller to energize the MR rotary damper in response to determining that the angular velocity exceeds an angular velocity threshold. The angular velocity threshold is associated with steering wheel jerk resulting from an off-road wheel impact.