We adapt the theory of extremely correlated Fermi liquids in two dimensions to study the phenomena of anisotropic elastoresistivity and dielectric response in high-Tc superconducting cuprates. There has been considerable focus on the nematic susceptibility in iron-based superconducting systems in recent years, but not much is known for cuprates. Motivated by these experiments, in part I, we calculate the in-plane elastoresistivity for optimally- and over-doped cuprates in the normal state. We present results for strain-induced anisotropic effects on the resistivity, the optical weight, and local density of states, and we additionally calculate their associated susceptibilities. Our quantitative predictions for these quantities have the prospect of experimental tests in the near future. In part II of this dissertation, inspired by recent experiments using inelastic electron scattering off the surface of cuprate materials to obtain {q,ω} dependence of the dielectric response, we study the t-J-Vc model in two dimensions. In this model in addition to the usual Hubbard-Gutzwiller short-range correlations, we add in the strong long-range correlations from Coulomb-type interactions on the tight-binding electrons. We calculate the {q,ω} dependent charge density fluctuations using the Green's function from extremely correlated Fermi liquid theory which is characterized by quasiparticle with a very small weight Z. Combining these properties with a novel set of formulae for the dynamical charge susceptibility and the dielectric constant that appropriately accounts for the physics of long-range Coulomb-type interactions in this model. We calculate the dynamical charge susceptibility χρρ(q,ω), (longitudinal) dielectric constant ε(q,ω), conductivity σ(q,ω), and plasma frequency for any q. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale Ωp which locates the peaks in Im χρρ(q,ω).