Over the last two decades, strong gravitational lensing has emerged as a potential method for studying the nature and distribution of dark matter on sub-galactic scales. In addition to the main lens substructure, line-of-sight dark matter haloes contribute greatly to the subtle perturbations of lensed images. Line-of-sight haloes, unlike dark matter subhaloes, imprint distinct anisotropic and quadrupole signatures in the maps that depict the divergence and curl of the effective deflection field, respectively, giving rise to quadrupole moments of the image-plane averaged two-point correlation function of these maps. In terms of central density evolution and dark matter halo distribution, the shapes and amplitudes of the two-point function multipoles alter dramatically in the presence of warm dark matter and self-interacting dark matter. This method, in conjunction with upcoming large-scale surveys, provides the prospect of improving the constraints on dark matter at a critical time in strong gravitational lensing research.