With the rapid proliferation of IoT devices, there has been some unprecedented surge in security breaches and forensic complexities attributable to the high data velocity, heterogeneity, and dynamic behavior of IoT networks. Existing forensic frameworks rely predominantly on static, batch-learning models which neither adapt to shifting threats, operate efficiently on resource-constrained devices, nor possess any capacity for real-time processing. In addition, current approaches inadequately satisfy the requirements for distributed environments, temporal consistency, and adaptive feature selection sets. This work, therefore, proposes an integrative Incremental Learning Framework for IoT Forensic Analysis, incorporating its five pioneering analytical models that will ensure real-time, scalable and adaptive forensic intelligence sets. The first model, Adaptive Multi-Agent Swarm-based Incremental Learning (AMASIL), introduces bioinspired agents using self-organizing particle dynamics to achieve dynamic threat learning. The second model will enable privacy-preserving, scalable analysis across distributed devices through hierarchical graph-based embeddings: Hierarchical Federated Forensic Graph Neural Network (HF2GNN). Third, Neuro-Synaptic Edge Cognitive Filtering (NECFiL) implements spiking neural networks at the edge for bioinspired temporal filtering of relevant forensic signals. Fourth, the Evolutionary Hypergraph Attention Learning (E-HAL) model is focused on deriving high-order feature relationships harnessed by an attention-driven hypergraph structure optimized through evolutionary heuristics. Finally, the Temporal Adversarial Forensic Consistency Network (TAFC-Net) assesses the robustness of learning in adversarial conditions using metrics of temporal consistency. The outcome is a 9.3% increased detection accuracy, 67% reduced feature space, and a 45% enhancement in edge throughput while leveraging the robust adaptation in data drift and poisoning. Also, the proposed models increased scalability, real-time responsiveness, and forensic precision and provide a very vital foundation for intelligent self-adaptive IoT forensic systems.