Space-Air-Ground integrated Vehicular Network (SAGVN) aims to achieve ubiquitous connectivity and provide abundant computational resources to enhance the performance and efficiency of the vehicular networks. Nonetheless, there are still challenges to overcome, including the scheduling of multilayered computational resources and the scarcity of spectrum resources. To address these problems, we propose a joint Task Offloading (TO) and Resource Allocation (RA) strategy in SAGVN (namely JTRSS). This strategy establishes an SAGVN model that incorporates air and space networks to expand the options for vehicular TO, and enhances the edge-computing resources of the system by deploying edge servers. To minimize the system average cost, we use the JTRSS algorithm to decompose the original problem into a number of subproblems. A maximum rate matching algorithm is used to address the channel allocation and the Lagrangian multiplier method is employed for computational RA. To acquire the optimal TO decision, a differential fusion cuckoo search algorithm is designed. Extensive simulation results demonstrate the significant superiority of the JTRSS algorithm in optimizing the system average cost.