Active optical modulation plays a pivotal role in the development of high-performance reconfigurable metasurfaces. The hybrid system of plasmonic nanostructures and epsilon-near-zero (ENZ) materials, which leverages both the near-field localization effect of plasmons and the tunable carrier concentration of ENZ materials, can serve as the key platform for realizing on-chip reconfigurable nanophotonic devices. In this study, we employ the finite element method (COMSOL Multiphysics) to numerically investigate the linear and nonlinear optical responses of a metasurface composed of an ultrathin indium tin oxide (ITO) film and U-shaped gold nanostructures placed atop it. A strong coupling exists between the SPR modes in the gold nanostructures and the ENZ modes in the ITO layer. By tuning the carrier concentration of ITO (N_ITO), the ENZ wavelength can be dynamically adjusted, thereby effectively controlling the resonance positions and linear transmission intensity. This enables an optical switching functionality in which the transmission can be modulated from "ON" to "OFF" at specific wavelengths. When the N_ITO is modulated from 9.7×10²⁰ cm^-3 to 4.9×10²⁰ cm^-3, the extinction ratio (ER) is up to 5.15 dB and -8.63 dB at the wavelength 1084 nm and 1203 nm, respectively. Beyond the modulation of linear optical responses, varying the N_ITO also allows control over the generation of second harmonic signals (SHG), achieving tunable nonlinear optical responses. The hydrodynamic model of metal and ITO is employed for the simulation of SHG responses. It is found that the SHG response is dominantly from the ITO layer and the conversion efficiency strongly depends on the matching between the ENZ modes and the surface plasmon resonances. The maximum SHG response can be obtained by optimizing N_ITO. When the N_ITO is changed from 1.12×10²¹ cm^-3 to 1.4×10²¹ cm^-3, the ER of SHG is up to 19.6 dB and -15.1 dB at the SHG wavelength 605 nm and 535 nm, respectively. These results demonstrate that metasurfaces based on plasmon-ENZ strong coupling offer a robust platform for dynamically modulating both linear and nonlinear optical responses in integrated nanophotonic devices.