Efficient dispersion of nanostructured fillers in thermoplastic polymers and elastomers remains an open challenge, and unless it is addressed, the potential utilization of conducting and magnetic fillers influencing the electronic properties of soft nanocomposites could not be properly assessed. Herein, we present a unique approach to address this challenge by constructing a microstructural fence using aligned magnetic networks of Ni nanowires in the direction of the applied external magnetic field, followed by flow-induced secondary in-planar alignment of multiwalled carbon nanotubes during the curing of the soft poly(dimethylsiloxane) (PDMS) elastomer. This mutually perpendicular arrangement offers unique magnetoconducting features to the soft elastomer matrix with moderately high conductivity, which is the key to superior electromagnetic shielding performance. The unique conformation of mutually perpendicular positions of both nanofillers in the bulk PDMS composites results in enhanced electromagnetic interference shielding performance (−28 dB) primarily through an absorption (80%) mechanism, driven primarily by the maximized interaction with incident electromagnetic waves inside the soft elastomer. Fundamental insights into the governing viscoelastic responses of these elastomer composites were gained through oscillatory rheological studies that investigate interparticle attraction within a quasi-solid network.