Plastic ionic molecular crystals are a novel class of materials that have attracted recent interest due to the discovery of ferroelectric and piezoelectric properties together with an orientationally disordered mesophase with high plasticity. Despite the growing interest, little is known about the mechanisms that underpin their piezoelectric properties. To address this knowledge gap, we study the dielectric, piezoelectric and elastic properties of eleven plastic ionic molecular crystals using van der Waals density functional theory. The piezoelectric coefficients were found to reach values comparable to inorganic piezoelectrics. Further, some plastic crystals have strikingly large piezoelectric anisotropies. For HQReO4 (Quinuclidinium perrhenate) an anisotropy of |d 16 /d 33 | = 119 was found, 11 times that of LiNbO3, a phase pure inorganic noted for its anisotropy. Our study links the anisotropy to rotational motion of the constituent molecules in response to shear stress. The large shear piezoelectric coefficients, yet modest dielectric permittivity results in coupling coefficients – a measure of its suitability for energy harvesting – with values up to 0.79. Our study points to the engineering of the rotational response of plastic ionic crystals as key to realizing the outstanding functional properties of these compounds.