Mental stress is known as a prime factor in road crashes. The devastation of these crashes often results in damage to humans, vehicles, and infrastructure. Likewise, persistent mental stress could lead to the development of mental, cardiovascular, and abdominal disorders. Preceding research in this domain mostly focuses on feature engineering and conventional machine learning approaches. These approaches recognize different levels of stress based on handcrafted features extracted from various modalities including physiological, physical, and contextual data. Acquiring good quality features from these modalities using feature engineering is often a difficult job. Recent developments in the form of deep learning (DL) algorithms have relieved feature engineering by automatically extracting and learning resilient features. This paper proposes different CNN and CNN-LSTSM-based fusion models using physiological signals (SRAD dataset) and multimodal data (AffectiveROAD dataset) for the driver’s two and three stress levels. The fuzzy EDAS (evaluation based on distance from average solution) approach is used to evaluate the performance of the proposed models based on different classification metrics (accuracy, recall, precision, F-score, and specificity). Fuzzy EDAS performance estimation shows that the proposed CNN and hybrid CNN-LSTM models achieved the first ranks based on the fusion of BH, E4-Left (E4-L), and E4-Right (E4-R). Results showed the significance of multimodal data for designing an accurate and trustworthy stress recognition diagnosing model for real-world driving conditions. The proposed model can also be used for the diagnosis of the stress level of a subject during other daily life activities.