IoT-based smart transportation monitors vehicles, cargo, and driver statuses for safe movement. Due to the limited computational capabilities of the sensors, the IoT devices require powerful remote servers to execute their tasks, and this phenomenon is called task offloading. Researchers have developed efficient task offloading and scheduling mechanisms for IoT devices to reduce energy consumption and response time. However, most research has not considered fault-tolerance-based job allocation for IoT logistics trucks, task and data-aware scheduling, priority-based task offloading, or multiple-parameter-based fog node selection. To overcome the limitations, we proposed a Multi-Objective Task-Aware Offloading and Scheduling Framework for IoT Logistics (MT-OSF). The proposed model prioritizes the tasks into delay-sensitive and computation-intensive tasks using a priority-based offloader and forwards the two lists to the Task-Aware Scheduler (TAS) for further processing on fog and cloud nodes. The Task-Aware Scheduler (TAS) uses a multi-criterion decision-making process, i.e., the analytical hierarchy process (AHP), to calculate the fog nodes' priority for task allocation and scheduling. The AHP decides the fog nodes' priority based on node energy, bandwidth, RAM, and MIPS power. Similarly, the TAS also calculates the shortest distance between the IoT-enabled vehicle and the fog node to which the IoT tasks are assigned for execution. A task-aware scheduler schedules delay-sensitive tasks on nearby fog nodes while allocating computation-intensive tasks to cloud data centers using the FCFS algorithm. Fault-tolerant manager is used to check task failure; if any task fails, the proposed system re-executes the tasks, and if any fog node fails, the proposed system allocates the tasks to another fog node to reduce the task failure ratio. The proposed model is simulated in iFogSim2 and demonstrates a 7% reduction in response time, 16% reduction in energy consumption, and 22% reduction in task failure ratio in comparison to Ant Colony Optimization and Round Robin.