The attitude, orbit, and shape control actuators of large space structures on orbits are functional overlapping and task coupled, resulting in actuator redundancy and high-energy consumption. This paper explores the integrated attitude–orbit–shape control problem of large space ring structures and proposes an online task switching and scheduling method for multiple actuators of space structures (OTSS-MASS). An adaptive allocation framework is proposed for the task switching of distributed actuators. The objectives of attitude–orbit–shape control are decomposed into attitude adjustment, orbit change, and shape maintenance tasks through a task decomposition algorithm. Task value estimation models are designed to guide a greedy task allocation of actuators. The adaptive allocation framework achieves online task reconfiguration for multiple distributed actuators, thereby enhancing the maneuverability of large space structures, improving actuator work efficiency, and reducing energy consumption in orbit. Simulation results demonstrate that OTSS-MASS outperforms the conventional actuator distribution methods. The overall effectiveness is improved by over 24% in terms of the comprehensive index, time index, trajectory index, and shape index.