Speech disorders affect an individual's ability to generate sounds or utilize the voice appropriately. Neurological, developmental, physical, and trauma may cause speech disorders. Speech impairments influence communication, social interaction, education, and quality of life. Successful intervention entails early and precise diagnosis to allow for prompt treatment of these conditions. However, clinical examinations by speech-language pathologists are time-consuming, subjective, and demand an automated speech disorder detection (SDD) model. Mel-spectrogram images present a visual representation of multiple speech disorders. By classifying Mel-Spectrogram, various speech disorders can be identified. In this study, the authors proposed an image classification-based automated SDD model to classify Mel-Spectrograms to identify multiple speech disorders. Initially, Wavelet Transform (WT) hybridization technique was employed to generate Mel-Spectrogram using the voice samples. A feature extraction approach was developed using an enhanced LEVIT transformer. Finally, the extracted features were classified using an ensemble learning (EL) approach, containing CatBoost and XGBoost as base learners, and Extremely Randomized Tree as a meta learner. To reduce the computational resources, the authors used quantization-aware training (QAT). They employed Shapley Additive Explanations (SHAP) values to offer model interpretability. The proposed model was generalized using Voice ICar fEDerico II (VOICED) and LANNA datasets. The exceptional accuracy of 99.1 with limited parameters of 8.2 million demonstrated the significance of the proposed approach. The proposed model enhances speech disorder classification and offers novel prospects for building accessible, accurate, and efficient diagnostic tools. Researchers may integrate multimodal data to increase the model's use across languages and dialects, refining the proposed model for real-time clinical and telehealth deployment.