Efficient distribution of active and reactive power in distribution networks is crucial for ensuring that consumer demand is met and that electrical power quality is maintained. This requires careful planning, particularly in terms of optimally placing and sizing distributed generator (DG) and capacitor bank (CB) units. These units play a key role in minimizing power losses and voltage fluctuations within the network. However, implementing DG and CB units in unbalanced distribution networks presents unique challenges due to inherent system unbalances. To address these challenges, this article proposes a method for allocating and sizing DG and CB units in unbalanced distribution networks. The approach accounts for the network's unbalance and targets multiple objectives, such as reducing power losses, improving multi-phase voltage stability, and minimizing phase-to-phase voltage unbalance. The fast and flexible radial power flow (FFRPF) technique is employed to model complex interactions and constraints within the network, leading to a multi-objective optimization problem. This optimization problem is solved using the weight aggregated particle swarm optimization (WA-PSO) method, a variant of particle swarm optimization tailored for multi-objective functions. WA-PSO simplifies the process by combining multiple objectives into a single function using weighted aggregation. The efficacy of this approach is validated on 19, 34, and 123-node unbalanced radial distribution networks (URDNs). The results show significant improvements in power delivery efficiency across all tested networks, especially when DG and CB units are operated simultaneously. Specifically, DG and CB integration led to a reduction in system losses by 89.90 %, 88.42 %, and 86.87 %, and a decrease in three-phase voltage unbalance indices by 88.75 %, 81.68 %, and 39.05 %, for the 19, 34, and 123-node systems, respectively, while maintaining voltage stability within acceptable limits. Additionally, CO2 emissions were reduced by 52 %, 62 %, and 53 % when microturbines were utilized instead of coal-based thermal power plants, further highlighting the environmental benefits of the proposed approach.