Transfer Learning (TL) is a powerful tool that enables robots to transfer learned policies across different environments, tasks, or embodiments. To further facilitate this process, efforts have been made to combine it with Learning from Demonstrations (LfD) for more flexible and efficient policy transfer. However, these approaches are almost exclusively limited to offline demonstrations collected before policy transfer starts, which may suffer from the intrinsic issue of covariance shift brought by LfD and harm the performance of policy transfer. Meanwhile, extensive work in the learning-from-scratch setting has shown that online demonstrations can effectively alleviate covariance shift and lead to better policy performance with improved sample efficiency. This work combines these insights to introduce online demonstrations into a policy transfer setting. We present Policy Transfer with Online Demonstrations, an active LfD algorithm for policy transfer that can optimize the timing and content of queries for online episodic expert demonstrations under a limited demonstration budget. We evaluate our method in eight robotic scenarios, involving policy transfer across diverse environment characteristics, task objectives, and robotic embodiments, with the aim to transfer a trained policy from a source task to a related but different target task. The results show that our method significantly outperforms all baselines in terms of average success rate and sample efficiency, compared to two canonical LfD methods with offline demonstrations and one active LfD method with online demonstrations. Additionally, we conduct preliminary sim-to-real tests of the transferred policy on three transfer scenarios in the real-world environment, demonstrating the policy effectiveness on a real robot manipulator.