In this paper, we propose a Satellite-Terrestrial Integrated Network (STIN) assisted vehicular multi-tier distributed computing (VMDC) system leveraging hybrid terahertz (THz) and radio frequency (RF) communication technologies. Task offloading for satellite edge computing is enabled by THz communication using the orthogonal frequency division multiple access (OFDMA) technique. For terrestrial edge computing, we employ non-orthogonal multiple access (NOMA) and vehicle clustering to realize task offloading. We formulate a non-convex optimization problem aimed at maximizing computation efficiency by jointly optimizing bandwidth allocation, task allocation, subchannel-vehicle matching and power allocation. To address this non-convex optimization problem, we decompose the original problem into four sub-problems and solve them using an alternating iterative optimization approach. For the subproblem of task allocation, we solve it by linear programming. To solve the subproblem of sub-channel allocation, we exploit many-to-one matching theory to obtain the result. The subproblem of bandwidth allocation of OFDMA and the subproblem of power allocation of NOMA are solved by quadratic transformation method. Finally, the simulation results show that our proposed scheme significantly enhances the computation efficiency of the STIN-based VMDC system compared with the benchmark schemes.