The Incident streams (IS) track is a research challenge aimed at finding important information from social media during crises for emergency response purposes. More specifically, given a stream of crisis-related tweets, the IS challenge asks a participating system to 1) classify what the types of users' concerns or needs are expressed in each tweet, known as the information type (IT) classification task and 2) estimate how critical each tweet is with regard to emergency response, known as the priority level prediction task. In this paper, we describe our multi-task transfer learning approach for this challenge. Our approach leverages state-of-the-art transformer models including both encoder-based models such as BERT and a sequence-to-sequence based T5 for joint transfer learning on the two tasks. Based on this approach, we submitted several runs to the track. The returned evaluation results show that our runs substantially outperform other participating runs in both IT classification and priority level prediction.