Observed El Niño-Southern Oscillation (ENSO) events exhibit distinct amplitude and evolution asymmetries due to nonlinear interactions between sea surface temperature (SST), equatorial zonal wind stress and thermocline depth anomalies. Establishment of atmospheric convection leads to a nonlinear response of zonal winds to SST, but its relative importance to nonlinear oceanic feedbacks remains unclear. Using a recharge oscillator model modified to incorporate various nonlinearities estimated from observations, we show that the nonlinear wind response to SST alone can induce a nonlinear response of the thermocline to winds and that of SST to the thermocline, as winds affect the growth of SST and damping of thermocline anomalies through the recharge/discharge process. Oceanic nonlinear feedbacks enhance the simulated ENSO asymmetries only when the nonlinear atmospheric feedback is present. Our result suggests that the observed strengthening of ENSO variability in the past century is attributable to an increase in the nonlinear atmospheric feedback.