With the integration of a high proportion of renewable energy into microgrids, distributed energy storage systems (DESS) play a crucial role in maintaining the stability and flexibility of power systems. Addressing the limitations of existing research, which often focuses on single control objectives and suffers from constrained convergence speeds, this paper proposes an efficient multi-task coordination framework based on momentum acceleration and Null-Space Based (NSB) control. First, focusing on the task of power allocation, a distributed update rule incorporating a momentum mechanism is developed, and explicit formulas for control parameters to achieve the optimal convergence rate are derived through theoretical analysis. Second, a multi-task coordination mechanism is established using the NSB method, where secondary tasks such as state-of-charge (SOC) balancing and voltage regulation are projected onto the null space of the power allocation task, thereby effectively avoiding control conflicts. Furthermore, a reinforcement learning algorithm is integrated to realize intelligent and dynamic task switching through the design of appropriate reward and penalty functions. Simulation results demonstrate that the proposed scheme significantly enhances the system"s convergence performance and operational reliability across multiple scenarios while ensuring precise power allocation.