Medical audio classification for lung abnormality diagnosis is a challenging problem owing to comparatively unstructured audio signals present in the respiratory sound clips. To tackle such challenges, we propose an ensemble model by incorporating diverse deep neural networks with attention mechanisms for undertaking lung abnormality and COVID diagnosis using respiratory, speech and coughing audio inputs. Specifically, four base deep networks are proposed which include attention-based Convolutional Recurrent Neural Network (A-CRNN), attention-based bidirectional Long Short-Term Memory (A-BiLSTM), attention-based bidirectional Gated Recurrent Unit (A-BiGRU), as well as Convolutional Neural Network (CNN). A Particle Swarm Optimization (PSO) algorithm is used to optimize training parameters of each network. An ensembling mechanism is used to integrate the outputs of these base networks by averaging their probability predictions of each class. Evaluated using respiratory ICBHI, Coswara breathing, speech, and cough datasets, as well as a combination of ICBHI and Coswara breathing databases, our ensemble model and base networks achieve ICBHI scores ranging from 0.920 to 0.9766. Most importantly, the empirical results indicate that a positive COVID diagnosis can be distinguished to a high degree from other more common respiratory diseases using audio recordings, based on the combined ICBHI and Coswara breathing datasets.