A centralized control mode is hopeless in satisfying the control requirement of a distribution network integrated with high penetration level of Distributed Generations (DGs), because of its low reliability, high computation and communication burden, and poor scalability. In considering the Var Compensators (VCs), this paper develops a multiple-object distributed control strategy for distribution networks utilizing the grouping of DGs and VCs based on the principle of distributed cooperative control. For the task of node voltage control, it develops a distributed control strategy that takes the capacity utilization ratio as the consensus variable for voltage control groups. Given the information on the imbalance of the power exchanged between the distribution network and the external power grid, it formulates a distributed control strategy that also takes capacity utilization ratio of VC as the consensus variable for reactive power control groups. As for the active power control, it proposes two control strategies that respectively take capacity utilization ratio and power factor as the consensus variables. A parameter tuning method for the three kinds of distributed control algorithms and the comparison of the two active power control strategies are presented. Simulation results on the IEEE14 nodes system are given to show the correctness and effectiveness of the proposed method. This work is supported by National Natural Science Foundation of China (No. 51877154).