In this study, a machine learning based method is proposed for creating synthetic eventful phasor measurement unit (PMU) data under time-varying load conditions. The proposed method leverages generative adversarial networks to create quasi-steady states for the power system under slowly-varying load conditions and incorporates a framework of neural ordinary differential equations (ODEs) to capture the transient behaviors of the system during voltage oscillation events. A numerical example of a large power grid suggests that this method can create realistic synthetic eventful PMU voltage measurements based on the associated real PMU data without any knowledge of the underlying nonlinear dynamic equations. The results demonstrate that the synthetic voltage measurements have the key characteristics of real system behavior on distinct time scales.