This work proposes a novel approach for sleep classification using the Sleep-EDFx Sleep Cassette-78 dataset, which includes EEG-based polysomnographies. The model uses a minimal feature set and hybrid neural networks for reliable classification. EEG signals are divided into 30-s epochs and balanced across sleep stages through downsampling. Ensemble Empirical Mode Decomposition (EEMD) is then applied to generate eight intrinsic mode functions (IMFs), from which statistical features—mean, standard deviation, variance, skewness, kurtosis, root mean square (RMS), and crest factor—are extracted, forming a 56-dimensional feature vector per epoch. The classification model combines a Graph Convolutional Network (GCN) for capturing spatial correlations with Bidirectional Long Short-Term Memory (BiLSTM) for modeling temporal dependencies. Despite using deep learning, the low-dimensional input keeps it efficient, achieving a macro F1 score of 0.77 on test data. This model preserves all six sleep stages defined in the original R&K annotation, enabling more granular analysis than common five-stage AASM-based approaches. Its efficiency makes it suitable for real-time use on resource-constrained devices such as wearables and mobile health platforms.