5G network will carry compute-intensive applications from vertical industries. Network slicing and edge computing are key technologies for fulfilling the diverse requirements of these applications efficiently. We define a cellular network with the edge computing capability as cellular edge computing network. Dynamically slicing a cellular edge computing network is challenging because it needs to orchestrate multi-domain resources and ensure isolation among network slices. In this paper, we present the VirtualEdge system that enables the dynamic creation of a virtual node (vNode) on top of a physical cellular edge computing node to serve the traffic and workloads of a network slice. VirtualEdge introduces a realizable multi-domain resource orchestration and virtualization that provides isolation among network slices without losing the efficiency in virtualizing the radio resources. To efficiently orchestrate multi-domain resources, we design a new learning-assisted algorithm that allows the resource orchestrator to optimize the utilization of physical resources without knowing the utility functions of individual vNodes. For the resource virtualization, we develop a heuristic algorithm and a credit-based queue management scheme to dynamically map virtual radio and computing resources to underlying physical resources, respectively. VirtualEdge is developed and implemented based on the OpenAirInterface LTE and CUDA GPU computing platforms, and its performance is validated through both experiments and large-scale simulations.