Social media sensing has emerged as a powerful sensing paradigm to collect the observations of the physical world by exploring the 'wisdom of crowd'. In this paper, we focus on a migratable disaster damage assessment problem in social media sensing applications. Our goal is to accurately identify the damage severity of affected areas in an unfolding disaster event using unlabeled social media data feeds (e.g., image posts on social media). Two fundamental challenges exist in solving our problem: i) different disaster events often have distinct characteristics (e.g., damage types, affected areas) that cannot be easily migrated; ii) it is non-Trivial to modify a damage assessment model from a previous event to adapt to a new event without using the labeled data from the new event. To address the above challenges, we develop SocialTrans, a hybrid deep transfer learning framework, to enable effective model migration for accurate damage assessment without using any training data from the studied disaster event. The evaluation results on four real-world disaster events show that SocialTrans consistently outperforms the state-of-The-Art baselines in accurately assessing the damage level of disasters.