This paper proposes a new stochastic multi-objective optimal energy management model named SMO-OEM model for techno-economic operations of smart distribution network (SDN) under uncertainty. A typical SDN is integrated with various generating resources such WTs, PVs, DGs, BESS, and utility grid to meet ever increasing and uncertain energy demands. A scenario-based analysis is utilized for handling the uncertainty allied with renewable energy generation (PVs and WTs), load power demand, and utility grid prices. In the first phase of the proposed model, several initial scenarios are generated with respect to day-ahead forecasts of PVs, WTs, load demand, grid prices using Monte-Carlo simulations and subsequently reduced them to finalize the input test scenarios for next phase. Thereafter, in the second phase, two conflicting objectives i.e. expected total operational cost ( $EF_{TC}$ ), and the expected total active power loss ( $EF_{TPL}$ ) are optimized simultaneously. The proposed SMO-OEM model recommends the further reactive support acquired from WTs, PVs, and BESS along with a demand response program (DRP) for optimum SDN operations. The proposed model is applied to two distinct sized networks i.e. modified IEEE-33 and IEEE-69 bus distribution networks and examined for different uncertainty ranges of ±5%, ±10%, and ±20% with respect to a day-ahead forecasted uncertain variables. Three comprehensive case studies are presented for detailed model assessments and comparisons under different uncertainty ranges. It is found that significant reductions are achieved in both $EF_{TC}$ and $EF_{TPL}$ by the recommended supplementary reactive management through WTs, PVs, and BESS. Additionally, DRP scheme is also applied at few locations to offer peak load reductions by shifting them to other timings over a period of 24 hours which further reduces both objectives ( $EF_{TC}$ and $EF_{TP}$ ). These recommendations are found suitable to significantly improve the bus voltage profile as well as economic operations.