Age of Information (AoI) is emerging as a novel metric for measuring information freshness in real-time monitoring systems. For computation-intensive status data, the information is not revealed until being processed. We consider a status update problem in a multi-source single-server system where the sources are scheduled to generate and transmit status data which are received and processed at the edge server. Generate-at-will sources with both random transmission time and process time are considered, introducing the joint optimization of source scheduling and status sampling on the basis of transmission-computation balancing. We show that a random scheduler is optimal for both non-preemptive and preemptive server settings, and the optimal sampler depends on the scheduling result and its structure remains consistent with the single-source system, i.e., threshold-based sampler for non-preemptive case and transmission-aware deterministic sampler for preemptive case. Then, the problem can be transformed to jointly optimizing the scheduling frequencies and the sampling thresholds/functions, which is non-convex. We proposed an alternation optimization algorithm to solve it. Numerical experiments show that the proposed algorithm can achieve the optimal in a wide range of settings.