The efficient utilization of heterogeneous computing systems is crucial for scientists and industrial organizations to execute computationally intensive applications. Task-based programming has emerged as an effective approach for harnessing the processing power of these systems. However, effective scheduling of task-based applications is critical for achieving high performance. Typically, these applications are represented as directed acyclic graphs (DAGs), which can be optimized through careful scheduling to minimize execution time and maximize resource utilization. In this paper, we introduce MultiPrio, a dynamic task scheduler that aims to minimize the overall completion time of parallelized task based applications. The goal is to find a trade-off between resource affinity, task criticality, and workload balancing on the resources. To this end, we compute scores for each task and manage the available tasks in the system with a data structure based on a set of priority queues. Tasks are assigned to available resources according to these scores, which are dynamically computed by heuristics based on task affinity and criticality. We also consider workload balancing across resources and data locality awareness. To evaluate the scheduler, we study the performance of dense and sparse linear algebra task-based applications and task-based FMM application using the StarPU runtime system on heterogeneous nodes. Our scheduler shows interesting results compared to other state-of-the-art schedulers in StarPU for regular applications, and excels at optimizing irregular workloads, improving performance by up to 31%.