Content delivery in vehicular edge networks faces critical challenges due to dynamic user mobility, unpredictable content request patterns, and limited storage at edge nodes. To tackle these problems, we propose a distributed online framework that jointly performs proactive caching at roadside units (RSUs) and hierarchical prefetching from the cloud to macro base stations (MBSs), enabling real-time adaptation to spatiotemporal variations in content demand across different time scales. Our goal is to minimize content transmission latency while satisfying system-wide resource and cost constraints. The proposed Vehicular-based Online Proactive caching and Prefetching (VOPP), integrates trajectory-based user mobility prediction with future content demand estimation to guide online distributed caching. At the RSU level, we formulate a distributed online convex optimization model with fine-grained gradient updates and inter-agent coordination based on real-time mobility patterns. At the MBS level, we construct a multi-step predicted content set using user mobility and request forecasts, and define a value density metric that combines popularity and delay reduction. On both levels, additional subsequent refinement steps ensure high-quality caching decisions. Extensive simulations based on a real-world GPS dataset of 10,357 taxi trajectories in Beijing demonstrate that VOPP significantly reduces transmission delay and achieves robust performance across diverse mobility patterns and user densities, outperforming baseline methods.