Acoustic event understanding and anomaly detection play a critical role in security monitoring, defence applications, and urban safety, yet current approaches struggle to generalise across noisy environments, rare event categories, and varying distances. To address these limitations, we propose a multi-domain, graph-integrated neural framework that unifies spectral, temporal, and phase representations for robust acoustic modeling. Our architecture combines a triple-stream decomposition - wavelet, gammatone, and complex spectrogram encoders - with a hierarchical cross-modal transformer for multi-scale fusion. Graph-theoretic feature integration, informed by physical propagation constraints, enables robust representation learning, while a memory-augmented contrastive module enhances recognition of rare events. The framework is trained with multi-task objectives encompassing classification, uncertainty-aware distance estimation, and environment-conditioned adaptation. Evaluations across seven benchmark datasets, including UrbanSound8K, ESC-50, FSD50K, DCASE, and MAD, demonstrate strong multi-task performance across classification, distance estimation, and uncertainty quantification. The framework achieves robust generalization under [Formula: see text] dB noise degradation with relative performance degradation below 12%, mean absolute error of [Formula: see text]m for controlled-condition distance estimation on datasets with ground-truth spatial annotatins (MAD, DCASE, MIMII), and [Formula: see text]m on ground-truth annotations from extended range intervals with aggregate MAE of 6.39m across all datasets inclusive of those with physics-simulation-derived labels and superior calibration ([Formula: see text] on primary benchmarks). Furthermore, the model achieves superior calibration and rare-event detection compared to leading transformer-based baselines. These results demonstrate that multi-domain, physics-aware acoustic modeling yields substantial robustness and multi-task advantages over single-task classification baselines, particularly under adverse environmental conditions and for rare event categories, with implications for real-time deployment in defense monitoring, disaster response, and smart city surveillance.