We report comparative experimental and theoretical studies of second and third harmonic generation from a 20nm-thick indium tin oxide layer in proximity of the epsilonnear-zero condition. Using a tunable OPA laser we record both spectral and angular dependence of the generated harmonic signals close to this particular point. In addition to the enhancement of the second harmonic efficiency close to the epsilon-near-zero wavelength, at oblique incidence third harmonic generation displays unusual behavior, predicted but not observed before. We implement a comprehensive, first-principles hydrodynamic approach able to simulate our experimental conditions. The model is unique, flexible, and able to capture all major physical mechanisms that drive the electrodynamic behavior of conductive oxide layers: nonlocal effects, which blueshift the epsilon-near-zero resonance by tens of nanometers; plasma frequency redshift due to variations of the effective mass of hot carriers; charge density distribution inside the layer, which determines nonlinear surface and magnetic interactions; and the nonlinearity of the background medium triggered by bound electrons. We show that by taking these contributions into account our theoretical predictions are in very good qualitative and quantitative agreement with our experimental results. We show that by taking these contributions into account our theoretical predictions are in very good qualitative and quantitative agreement with our experimental results. We expect that our results can be extended to other geometries where ENZ nonlinearity plays an important role.; in ε and out ε are the dielectric constants inside and outside the medium, respectively; z in E and z out E are the corresponding longitudinal components of the electric field amplitude, and require oblique incidence to excite the ENZ point. Therefore, if in ε decreases, then z in E increases and nonlinear optical phenomena are enhanced, including nonlinear index of refraction [1], harmonic generation, optical bistability, and soliton excitation [2-13].While ENZ materials can be made artificially, all natural bulk materials that display a Lorentz-like response also exhibit a real part of the dielectric permittivity that crosses zero, in