Coupled dynamics between westerly wind events (WWEs) and the El Niño–Southern Oscillation (ENSO) is examined using an atmosphere–ocean coupled model with intermediate complexity. The model incorporates state-dependent stochastic noise that mimics observed WWEs, which occur at the edge of the Pacific warm pool when the Niño-4 sea surface temperature (SST) anomaly increases positively. The model parameter that controls the efficiency of the thermocline feedback, γ, is perturbed to elaborate the sensitivity of the results to the system’s stability. Without the noise (experiment NO), the model produces an ENSO-like regular oscillation with a 6-yr period, the variance of which increases with γ. When additive noise is introduced over the western Pacific (experiment AD), the oscillations become irregular with a dominant period of 4–6 years and the increase in the variance relative to the NO experiment depends on γ. When state-dependent noise is included (experiment SD), the oscillatory solution is also irregular, and its variance and asymmetry are increased irrespective of the value of γ. Both the additive and state-dependent noise contribute to the occurrence of two types of variability, corresponding to the eastern Pacific (EP) and central Pacific (CP) El Niños. In SD, the state dependence of the stochastic noise guarantees the existence of CP El Niño regardless of γ since the increased likelihood of WWE occurrence with Niño-4 SSTs results in a positive feedback in the central Pacific. The above results suggest that the state dependence of WWEs plays a crucial role in the asymmetry and diversity of ENSO.