This paper proposes an online hierarchical volt/var control (VVC) for unbalanced distribution networks using diagonal-scaling alternating direction method of multipliers (DS-ADMM). Under the hierarchical VVC strategy, local photovoltaic (PV) agents only exchange limited information with the center agent and adjust reactive power outputs in real time, with the goal of minimizing the voltage deviations and reactive power regulation costs in the time-varying environment. A diagonalized auxiliary matrix is constructed and developed from the Hessian matrix using preconditioning methods, which is then combined with alternating direction method of multipliers (ADMM) to design the DS-ADMM with improved convergence speed. The DS-ADMM is applied to the hierarchical VVC strategy, further improving the tracking capability and performance for time-varying environmental changes. Simulation studies on a modified IEEE 123-bus unbalanced distribution network are conducted to verify the effectiveness of the hierarchical VVC strategy using DS-ADMM and its robustness under non-ideal communication conditions, and its scalability is further validated on the modified IEEE 8500-node test feeder.