Recently, with the significant growth of load demand, further interest in renewable energy sources (RESs) incorporated into electric distribution systems (DSs) has become important. However, the output powers' stochastic fluctuations of the photovoltaic (PV) and wind turbine (WT) generation sources, as well as the load demand, result in obvious operational challenges related to the reliability and line loading of these systems. Therefore, this present study is intended to enhance the load-oriented reliability indices (LORIs), the customer-oriented reliability indices (CORIs), and the line loading index (LLI) of the DSs by assigning the optimal integration of RESs and compressed air energy storages (CAESs) through the determination of both the optimal placement and capacities of RESs and CAESs simultaneously, as well as the optimal charging and discharging powers of the CAESs and their initial state of charge based on the red-tailed hawk (RTH) optimization technique. The Monte Carlo Simulation (MCS) and the Scenario-based Reduction (SBR) uncertainty methods are implemented to address the uncertainties of RESs and loading. The influences of the linear failure rate of DS's feeders and the installation of protective devices are also demonstrated. The efficiency of the intended methodology is demonstrated on the IEEE 69-bus and IEEE 33-bus DSs associated with voltage-dependent, time-varying mixed loads. The outcomes obtained from the suggested RTH are compared to those of other reported optimization techniques to validate its effectiveness. The results reveal that the optimal integration of RESs along with CAESs in the IEEE 69-bus test DS can improve the energy not supplied (ENS), system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI), average service unavailability index (ASUI), and LLI by 1.09 %, 1.86 %, 1.73 %, 1.89 %, and 64.53 %, respectively.