Medical image analysis typically includes several tasks such as enhancement, segmentation, and classification. Traditionally, these tasks are implemented using separate deep learning models for separate tasks, which is not efficient because it involves unnecessary training repetitions, demands greater computational resources, and requires a relatively large amount of labeled data. In this paper, we propose a multi-task training approach for medical image analysis, where individual tasks are fine-tuned simultaneously through relevant knowledge transfer using a unified modality-specific feature representation (UMS-Rep). We explore different fine-tuning strategies to demonstrate the impact of the strategy on the performance of target medical image tasks. We experiment with different visual tasks (e.g., image denoising, segmentation, and classification) to highlight the advantages offered with our approach for two imaging modalities, chest X-ray and Doppler echocardiography. Our results demonstrate that the proposed approach reduces the overall demand for computational resources and improves target task generalization and performance. Further, our results prove that the performance of target tasks in medical images is highly influenced by the utilized fine-tuning strategy.