A variety of novel mobile applications are developed to attract the interests of potential users in the emerging 5G-enabled vehicular networks. Although computation offloading and task scheduling have been widely investigated, it is rather challenging to decide the optimal offloading ratio and perform adaptive task scheduling in high-dynamic networks. Furthermore, the scheduling policy made by the network operator may be violated, since vehicular users are rational and selfish to maximize their own profits. By considering the incentive compatibility and individual rationality of vehicular users, we present POETS, an efficient partial computation offloading and adaptive task scheduling algorithm to maximize the overall system-wide profit. Specially, a two-sided matching algorithm is first proposed to derive the optimal transmission scheduling discipline. After that, the offloading ratio of vehicular users can be obtained through convex optimization, without any information of other users. Furthermore, a non-cooperative game is constructed to derive the payoff of vehicular users that can reach the equilibrium between users and the network operator. Theoretical analyses and performance evaluations based on real-world traces of taxies demonstrate the effectiveness of our proposed solution.