With advancements in integrated space–air–ground global observation capabilities, the volume of remote sensing data is experiencing exponential growth. Traditional computing models can no longer meet the task processing demands brought about by the vast amounts of remote sensing data. As an important means of processing remote sensing data, distributed cluster computing’s task scheduling directly impacts the completion time and the efficiency of computing resource utilization. To enhance task processing efficiency and optimize the allocation of computing resources, this study proposes a Multi-Strategy Improved Siberian Tiger Optimization (MSSTO) algorithm based on the original Siberian Tiger Optimization (STO) algorithm. The MSSTO algorithm integrates the Tent chaotic map, the Lévy flight strategy, Cauchy mutation, and a learning strategy, showing significant advantages in convergence speed and global optimal solution search compared to the STO algorithm. By combining stochastic key encoding schemes and uniform allocation encoding schemes, taking the task scheduling of aerosol optical depth retrieval as a case study, the research results show that the MSSTO algorithm significantly shortens the completion time (21% shorter compared to the original STO algorithm and an average of 15% shorter compared to nine advanced algorithms, such as a particle swarm algorithm and a gray wolf algorithm). It demonstrates superior solution accuracy and convergence speed over various competing algorithms, achieving the optimal execution sequence and machine allocation scheme for task scheduling.