This paper presents a novel 3D lattice metastructure featuring customizable elastic moduli in all three dimensions, achieved through distorted Kelvin cells. These structures are fabricated using thermoplastic polyurethane (TPU) materials through selective laser sintering (SLS) additive manufacturing techniques. Static compression tests reveal significant recoverable deformations and near-zero Poisson effects. Numerical simulations indicate that distorted Kelvin cells (DKCs) exhibit lower transmission in the longitudinal direction compared to standard Kelvin cells within the frequency range of interest. Additionally, DKCs demonstrate increased coupling between longitudinal and transverse directions at resonant frequencies. Parametric studies explore various lattice sizes, face configurations (closed or open), twisting angles, and matrix materials. Optimization studies, focusing on different twisting angles on each pair's faces, aim to minimize the response under 400 Hz, showcasing the potential for tuning these structures for specific applications.