One of the most common and challenging medical conditions to deal with in old-aged people is the occurrence of knee osteoarthritis (KOA). Manual diagnosis of this disease involves observing X-ray images of the knee area and classifying it under five grades using the Kellgren-Lawrence (KL) system. This requires the physician's expertise, suitable experience, and a lot of time, and even after that the diagnosis can be prone to errors. Therefore, researchers in the ML/DL domain have employed the capabilities of deep neural network (DNN) models to identify and classify KOA images in an automated, faster, and accurate manner. To this end, we propose the application of six pretrained DNN models, namely, VGG16, VGG19, ResNet101, MobileNetV2, InceptionResNetV2, and DenseNet121 for KOA diagnosis using images obtained from the Osteoarthritis Initiative (OAI) dataset. More specifically, we perform two types of classification, namely, a binary classification, which detects the presence or absence of KOA and secondly, classifying the severity of KOA in a three-class classification. For a comparative analysis, we experiment on three datasets (Dataset I, Dataset II, and Dataset III) with five, two, and three classes of KOA images, respectively. We achieved maximum classification accuracies of 69%, 83%, and 89%, respectively, with the ResNet101 DNN model. Our results show an improved performance from the existing work in the literature.