Internet of Things (IoT) can significantly enhance various aspects of today&rsquo / s electric power grid infrastructures for making reliable, efficient, and safe next-generation Smart Grids (SGs). However, harsh and complex power grid infrastructures and environments reduce the accuracy of the information propagating through IoT platforms. In particularly, information is corrupted due to the measurement errors, quantization errors, and transmission errors. This leads to major system failures and instabilities in power grids. Redundant information measurements and retransmissions are traditionally used to eliminate the errors in noisy communication networks. However, these techniques consume excessive resources such as energy and channel capacity and increase network latency. Therefore, we propose a novel statistical information fusion method not only for structural chain and tree-based sensor networks, but also for unstructured bidirectional graph noisy wireless sensor networks in SG environments. We evaluate the accuracy, energy savings, fusion complexity, and latency of the proposed method by comparing the said parameters with several distributed estimation algorithms using extensive simulations proposing it for several SG applications. Results prove that the overall performance of the proposed method outperforms other fusion techniques for all considered networks. Under Smart Grid communication environments, the proposed method guarantees for best performance in all fusion accuracy, complexity and energy consumption. Analytical upper bounds for the variance of the final aggregated value at the sink node for structured networks are also derived by considering all major errors.