Architected materials typically derive their mechanical properties from the geometry of bonded truss networks. However, a distinct class of materials emerges when connectivity is defined by topological entanglement rather than rigid joints. This work investigates 3D architected materials composed of intertwined helical filaments, where the global mechanical response is dictated by the intricate interplay between internal topology and localized geometric constraints. We present a systematic study on the influence of nodal topology-defined by the number of intertwined filaments and their braiding patterns–alongside a multi-parameter geometric space including fiber radius, helix radius, and wavelength. Using computational simulations, we characterize the mechanical response across two distinct regimes: the initial compliant phase and the large-deformation regime characterized by mechanical locking. Our results reveal that the onset of mechanical locking is highly sensitive to the node topology and the ratio of fiber-to-helix radii, which govern the redistribution of stress and the internal frictional dynamics. We demonstrate that by tuning these topological and geometric parameters, one can program the stiffness and the densification strain of the network. This research establishes a framework for the inverse design of reconfigurable, entangled materials that utilize topological interlocking to achieve high energy absorption and tunable nonlinearity.