Sparse-View Computed Tomography (SVCT) offers low-dose and fast imaging but suffers from severe artifacts. Optimizing the sampling strategy is an essential approach to improving the imaging quality of SVCT. However, current methods typically optimize a universal sampling strategy for all types of scans, overlooking the fact that the optimal strategy may vary depending on the specific scanning task, whether it involves particular body scans (e.g., chest CT scans) or downstream clinical applications (e.g., disease diagnosis). The optimal strategy for one scanning task may not perform as well when applied to other tasks. To address this problem, we propose a deep learning framework that learns task-specific sampling strategies with a multi-task approach to train a unified reconstruction network while tailoring optimal sampling strategies for each individual task. Thus, a task-specific sampling strategy can be applied for each type of scans to improve the quality of SVCT imaging and further assist in performance of downstream clinical usage. Extensive experiments across different scanning types provide validation for the effectiveness of task-specific sampling strategies in enhancing imaging quality. Experiments involving downstream tasks verify the clinical value of learned sampling strategies, as evidenced by notable improvements in downstream task performance. Furthermore, the utilization of a multi-task framework with a shared reconstruction network facilitates deployment on current imaging devices with switchable task-specific modules, and allows for easily integrate new tasks without retraining the entire model.