Sleep is an integral and vital component of human life, contributing significantly to overall health and well-being, but a considerable number of people worldwide experience sleep disorders. Sleep disorder diagnosis heavily depends on accurately classifying sleep stages. Traditionally, this classification has been performed manually by trained sleep technologists that visually inspect polysomnography records. However, in order to mitigate the labor-intensive nature of this process, automated approaches have been developed. These automated methods aim to streamline and facilitate sleep stage classification. This study aims to classify sleep stages in a dataset comprising subjects with insomnia, PLM, and sleep apnea. The dataset consists of PSG recordings from the multi-ethnic study of atherosclerosis (MESA) cohort of the national sleep research resource (NSRR), including 2056 subjects. Among these subjects, 130 have insomnia, 39 suffer from PLM, 156 have sleep apnea, and the remaining 1731 are classified as good sleepers. This study proposes an automated computerized technique to classify sleep stages, developing a machine-learning model with explainable artificial intelligence (XAI) capabilities using wavelet-based Hjorth parameters. An optimal biorthogonal wavelet filter bank (BOWFB) has been employed to extract subbands (SBs) from 30 seconds of electroencephalogram (EEG) epochs. Three EEG channels, namely: Fz_Cz, Cz_Oz, and C4_M1, are employed to yield an optimum outcome. The Hjorth parameters extracted from SBs were then fed to different machine learning algorithms. To gain an understanding of the model, in this study, we used SHAP (Shapley Additive explanations) method. For subjects suffering from the aforementioned diseases, the model utilized features derived from all channels and employed an ensembled bagged trees (EnBT) classifier. The highest accuracy of 86.8%, 87.3%, 85.0%, 84.5%, and 83.8% is obtained for the insomniac, PLM, apniac, good sleepers and complete datasets, respectively. Using these techniques and datasets, the study aims to enhance sleep stage classification accuracy and improve understanding of sleep disorders such as insomnia, PLM, and sleep apnea.