The linear elasticity of dilute colloidal gels formed from discoidal latex particles is quantified as a function of aspect ratio and modeled by confocal microscopy characterization of their fractal cluster microstructure. Colloidal gels are of fundamental interest because of their widespread use to stabilize complex fluids in industry. Technological interest in producing gels of desired moduli using the least number of particles drives formulators to produce gels at dilute concentrations. However, dilute gels self-assembled from isotropic spheres offer limited scope for rheological tunability due to the universal characteristics of their fractal microstructure. Our results show that changing the building block shape from sphere to discoid yields very large shifts in gel elasticity relative to the universal behavior reported for spheres. This shift - tunable through aspect ratio - yields up to a 100-fold increase in elastic modulus at a fixed volume fraction. From modeling the results using the theory for fractal cluster gel rheology, which is applicable at the dilute conditions of this study, we reveal that the efficient generation of elasticity by the colloidal discoids is the consequence of the combined effects of shape anisotropy on the fractal microstructure of the gel network, the anisotropy of the attractive interparticle pair potentials, and the volumetric compactness of the fractal cluster. These results extend prior characterizations of the rheology of non-spherical particulate gels by providing quantitative estimates of how the specific mechanisms of fractality, pair potential, and clustering mediate the profound effects of particle shape anisotropy on the elastic rheology of colloidal gels.