Insomnia, a prevalent sleep disorder, adversely impacts cognitive and physical health, highlighting the need for accurate and efficient diagnostic tools. This study employs multimodal biosignal analysis, integrating EEG, EMG, EOG, and ECG to classify individuals as insomniac or non-insomniac. Preprocessing techniques, such as resampling, are applied to reduce computational load, followed by feature extraction methods tailored to each signal modality. These methods capture frequency-domain, time-domain and entropy metrics, which reveal physiological traits associated with insomnia, such as irregular brain activity, altered muscle atonia, and abnormal eye movements. Early and late fusion techniques are employed for the classification task and early fusion achieved a comparatively better result of 95% than late fusion of 92.275% with an highest overall F1 score of 95%. Explainable AI concepts such as Local Interpretable Model Agnostic Explanations (LIME) and Shapley Additive exPlanations (SHAP) were used to find out which features show more significance for classification. By leveraging multimodal data fusion, this methodology captures intricate physiological interactions that improve diagnosis of the disease and provides a non-invasive, detection of insomnia, paving way for the enhanced therapeutic interventions.