This work attempts to design an effective sleep staging system, making the best use of the available signals, strategies, and features in the literature. It must not only perform well on different datasets comprising healthy and clinical populations but also achieve good accuracy in cross-dataset experiments. Toward this end, we propose a model comprising multiple binary classifiers in a hierarchical fashion, where, at each level, one or more of EEG, EOG, and EMG are selected to best differentiate between two sleep stages. The best set of 100 features is chosen out of all the features derived from selected signals. The class imbalance in data is addressed by random undersampling and boosting techniques with decision trees as weak learners. Temporal context and data augmentation are used to improve the performance. We also evaluate the performance of our model by training and testing on different datasets. We compare the results of five approaches: using only EEG, EEG+EOG, EEG+EMG+EOG, EEG+EMG, and selective modality with a specific combination of EEG, EMG, and/or EOG at each level. The best results are obtained by considering features from EEG+EMG+EOG at each hierarchical level. The proposed model achieves average accuracies of 83.1%, 90.0%, 84.4%, 82.1%, 81.5%, 79.9%, and 73.7% on Sleep-EDF, Exp Sleep-EDF, ISRUC-S1, S2 and S3, DRMS-SUB, and DRMS-PAT datasets, respectively. For all the datasets except DRMS-SUB, the proposed method outperforms all the state-of-the-art approaches. Cross-dataset performance exceeds 80% for all datasets except DRMS-PAT; independent of whether the test data is from normal subjects or patients.