Background/Objectives: Obstructive sleep apnea (OSA) is a common and serious sleep-related disorder that causes repeated interruptions in breathing during sleep. Traditional diagnostic methods, such as polysomnography, are accurate but costly, time-consuming, and unsuitable for large-scale screening. This study proposes and evaluates a lightweight diagnostic framework based on an Extreme Learning Machine (ELM) optimized by a set of basic and advanced metaheuristic optimizers (GA, RUN, MEO, CL-PSO, HI-WOA, GWO, HGS, HHO, SeaHO, MGO, and the hybrid GWO--WOA). The model aims to improve early detection of OSA using demographic and clinical data. Methods: Two real datasets were employed to train and evaluate the proposed framework: (i) a clinical OSA dataset with 274 subjects and 31 demographic/anthropometric and sleep-related predictors, and (ii) a public strongly imbalanced Sleep-Disordered Breathing (SDB) dataset with 500 subjects and 10 structured predictors. Metaheuristic algorithms are used to optimize ELM weights and biases, addressing the instability of random initialization and improving model generalization. The optimized models are evaluated against eight baseline classifiers, including Logistic Regression (LR), k-nearest neighbours (KNN), Decision Tree (DT), Random Forest (RF), Support Vector Machine (SVM), Multilayer Perceptron (MLP), XGBoost (XGB), and a standard ELM classifier. Results: Results show that metaheuristic optimization improves ELM on the OSA dataset, increasing ROC-AUC from 0.6527 to about 0.73 and accuracy from 0.6573 to about 0.69–0.70, while on the highly imbalanced SDB dataset, it yields modest ROC-AUC gains (from 0.5132 to about 0.544–0.548) with small decreases in accuracy and F1-score. Conclusions: The proposed framework provides a fast, lightweight, and cost-effective screening tool for large-scale, resource-limited healthcare settings, enabling early OSA detection and preventive intervention.