In this paper, we study a network slicing problem for edge-cloud orchestrated vehicular networks, in which the edge and cloud servers are orchestrated to process computation tasks for reducing network slicing cost while satisfying the quality of service requirements. We propose a two-stage network slicing framework, which consists of 1) network planning stage in a large timescale to perform slice deployment, edge resource provisioning, and cloud resource provisioning, and 2) network operation stage in a small timescale to perform resource allocation and task dispatching. Particularly, we formulate the network slicing problem as a two-timescale stochastic optimization problem to minimize the network slicing cost. Since the problem is NP-hard due to coupled network planning and network operation stages, we develop a Two timescAle netWork Slicing (TAWS) algorithm by collaboratively integrating reinforcement learning (RL) and optimization methods, which can jointly make network planning and operation decisions. Specifically, by leveraging the timescale separation property of decisions, we decouple the problem into a large-timescale network planning subproblem and a small-timescale network operation subproblem. The former is solved by an RL method, and the latter is solved by an optimization method. Simulation results based on real-world vehicle traffic traces show that the TAWS can effectively reduce the network slicing cost as compared to the benchmark scheme.