The space-air-ground integrated vehicular networks (SAGVN) has significant advantages in satisfying the requirements of the Internet of Vehicles (IoV) business for wide area coverage and long-distance communications. However, the multi-dimensional nature of the SAGVN leads to diverse network resources, it is necessary to provide different services for various scenarios, which makes the problem of network resource allocation becomes extremely challenging. In this paper, we focus on the resource allocation of small cells in SAGVN. Specifically, the user association is considered to optimize connection between base stations and vehicles. On this basis, a subchannel and power allocation method is designed. The proposed subchannel allocation scheme ensures that users can obtain the maximum gain on its subchannel, and the Lagrangian duality theory is introduced to solve the power allocation problem. Meanwhile, the edge computing is applied to the SAGVN, and the vehicles can offload the local tasks to the edge server. In order to reduce the delay in the offloading process, taking the time delay as a constraint condition can further optimize the communication performance. The simulation results show that the proposed scheme can effectively improve the sum rate of small cells in SAGVN, and the performance is better than existing algorithms.