The control of nonlinear optical responses in van der Waals ferroelectrics at the nanoscale offers opportunities for developing two-dimensional integrated nanophotonics with programmable functionalities. In this work, we report the first realization of nanoscale nonvolatile control of the amplitude and polarization of second-harmonic generation (SHG) response in layered CuInP2S6 (CIPS) via the domain structure in an interfacial PbZr0.2Ti0.8O3 (PZT) thin film. The SHG intensity at CIPS/PZT heterointerface is continuously modulated, either substantially enhanced or almost entirely quenched, by the circular domain walls in underlying ferroelectric oxide. The interfacial coupling of CIPS polar axis with in-plane polarization of PZT domain walls tailors the SHG light polarization into two-fold (C2V) symmetry, which is well modeled by nonlinear electromagnetic theory. Overall, this study enables nonvolatile programmable design of nonlinear light intensity and polarization in van der Waals ferroelectrics at the nanoscale.