Directional assembly of nanoscale objects results in morphologies that can broadly be classified as supra-molecular nanopolymers. Such morphologies, given a functional choice of the monomers used as building blocks, can be of ubiquitous utility in optical, magnetic, rheological, and medical applications. These applications, however, require a profound understanding of the interplay between monomer shape and bonding on one side, and polymeric properties - on the other. Recently, we fabricated nanopolymers using cuboid DNA nanochambers, as they not only allow fine-tuning of the resulting morphologies but can also carry magnetic nanoparticles. However, it is not known if the cuboid shape and inter-cuboid connectivity restrict the equilibrium confirmations of the resulting nanopolymers, making them less responsive to external stimuli. In this work, using Molecular Dynamics simulations, we perform an extensive comparison between various nanopolymer architectures to explore their polymeric properties, and their response to an applied magnetic field if magnetic nanoparticles are embedded. We explain the impact of monomer shape and bonding on the mechanical and magnetic properties and show that DNA nanochambers can build highly responsive and magnetically controllable nanopolymers.