When introducing a nanoparticle into an optical trap, its mass and shape are not immediately apparent. We combine a charge-based mass measurement with a shape determination method based on light scattering and an analysis of the damping rate anisotropy, all on the same set of silica nanoparticles, trapped using optical tweezers in vacuum. These methods have previously only been used separately, and the mass determination method has not been applied to asymmetric particles before. We demonstrate that the combination of these classification techniques is required to distinguish particles with similar mass but different shape, and vice versa. The ability to identify these parameters is a key step for a range of experiments on precision measurements and sensing using optically levitated nanoparticles.