Latency- and energy-efficient task offloading is essential for V2X-enabled vehicular edge computing, where heterogeneous onboard applications compete for limited helper-vehicle and roadside-unit resources. This paper proposes a task-type-aware stable matching offloading framework for needing vehicles (NVs). Each task is partitioned into subtasks that can be executed locally, offloaded to nearby helper vehicles (HVs), or offloaded to roadside units (RSUs). Type-dependent utilities combine normalised completion latency and NV-side energy to capture the different requirements of latency-critical, computation-intensive, and delay-tolerant subtasks. The resulting many-to-one deferred acceptance mechanism assigns subtasks to providers under feasibility and quota constraints, with local fallback or deferral when no suitable provider is available. Monte-Carlo simulations show that the proposed task-type-aware stable matching (TA-SM) scheme reduces average latency and NV-side energy and improves deadline satisfaction compared with greedy offloading, RSU-only offloading, Spider Monkeys Optimization (SMO), and task-unaware stable matching (TU-SM).