In this article, we address the fault detection and classification problem in induction motors through a multi-stage feature extraction approach and transfer learning. Our proposed method involves obtaining the Continuous Wavelet Transform of transient stator current under various operating and fault conditions, considering the number of broken bars. The resulting scalograms are then fed into two deep convolutional neural networks, ResNet-18 and ResNet-50, pre-trained on large datasets, to extract features from the obtained images. The extracted deep features are then fused and employed for fault classification using a Support Vector Machine and Ensemble Decision Tree. The experimental results, conducted on a comprehensive dataset, demonstrate that the proposed method with multi-stage feature extraction and fused deep features significantly enhances the accuracy of fault detection and classification in induction motors. In addition, the results were taken on a downsampled dataset to verify the practicality of the proposed approach when using low-cost data acquisition systems.