<p>Energy-efficient real-time monitoring of physiological parameters is a fundamental requirement in smart healthcare environments, where continuous patient observation, low latency, and reliable clinical decision support are critical. However, conventional cloud-centric healthcare systems suffer from high communication overhead, delayed response, and increased energy consumption, which limit their effectiveness in time-sensitive medical scenarios. To address these limitations, this manuscript proposes an intelligent and energy-efficient Edge-IoT architecture for monitoring and analysis of vital signs in smart healthcare using Steerable Diffusion Attention Graph Neural Networks (EIoT-VS-SDAGNN). Initially, the physiological data are collected from the MIMIC-III Clinical Database, comprising Intensive Care Unit (ICU) patient vital signs such as heart rate, blood pressure, respiratory rate, temperature, and SpO₂. Preprocessing of data is done via the agdPLS (adaptive extended Gaussian peak derivative reweighted penalized least squares) algorithm that helps in removing noise and irregularities from the data. Subsequently, an effective hybrid feature selection strategy, namely Forward-Escape Cuckoo Catfish Optimization (FE-CCO), which combines the Forward-Escape Algorithm (FEA) and Cuckoo Catfish Optimizer (CCO), is employed to select the most relevant physiological features while reducing computational complexity for edge deployment. The optimized feature set is then fed into a hybrid deep learning architecture integrating a Steerable Graph Neural Network (SGNN) with a Diffusion Kernel Attention Network (DKAN), collectively referred to as SDAGNN, to detect abnormal physiological patterns and classify patient health status into Normal, Mild, Moderate and Critical categories. To further enhance convergence stability and classification performance, a Comment Feedback Optimization Algorithm (CFOA) is applied for hyperparameter tuning. The trained model is deployed within the proposed Health-EoTs edge environment to enable low-latency abnormality detection and real-time alert generation. At the same time, summarized health records are securely stored in the cloud for continuous monitoring and long-term analysis. The proposed EIoT-VS-SDAGNN framework is evaluated based on Accuracy, Precision, Recall, F1-score, Specificity and ROC. Experimental results demonstrate that EIoT-VS-SDAGNN achieves 99.21% higher Accuracy and 4.5% False Alarm Rate (FAR) compared to existing abnormal physiological patterns detection approaches.</p>