Traffic forecasting, which benefits from mobile Internet development and position technologies, plays a critical role in Intelligent Transportation Systems. It helps to implement rich and varied transportation applications and bring convenient transportation services to people based on collected traffic data. Most existing methods usually leverage graph-based deep learning networks to model the complex road network for traffic forecasting shallowly. Despite their effectiveness, these methods are generally limited in fully capturing high-order spatial dependencies caused by road network topology and high-order temporal dependencies caused by traffic dynamics. To tackle the above issues, we focus on the essence of traffic system and propose STHODE: Spatio-Temporal Hypergraph Neural Ordinary Differential Equation Network, which combines road network topology and traffic dynamics to capture high-order spatio-temporal dependencies in traffic data. Technically, STHODE consists of a spatial module and a temporal module. On the one hand, we construct a spatial hypergraph and leverage an adaptive MixHop hypergraph ODE network to capture high-order spatial dependencies. On the other hand, we utilize a temporal hypergraph and employ a hyperedge evolving ODE network to capture high-order temporal dependencies. Finally, we aggregate the outputs of stacked STHODE layers to mutually enhance the prediction performance. Extensive experiments conducted on four real-world traffic datasets demonstrate the superior performance of our proposed model compared to various baselines.