COVID-19, chronic obstructive pulmonary disease (COPD), heart failure (HF), and pneumonia can lead to acute respiratory deterioration. Prompt and accurate diagnosis is crucial for effective clinical management. Chest X-ray (CXR) and chest computed tomography (CT) are commonly used for confirming the diagnosis, but they can be time-consuming and biased. To address this, we developed a computationally efficient deep feature engineering model called Hybrid-Patch-Alex for automated COVID-19, COPD, and HF diagnosis. We utilized one CXR dataset and two CT image datasets, including a newly collected dataset with four classes: COVID-19, COPD, HF, and normal. Our model employed a hybrid patch division method, transfer learning with pre-trained AlexNet, iterative neighborhood component analysis for feature selection, and three standard classifiers (k-nearest neighbor, support vector machine, and artificial neural network) for automated classification. The model achieved high accuracy rates of 99.82%, 92.90%, and 97.02% on the respective datasets, using kNN and SVM classifiers.