This work focuses on the analysis of Italian social media messages for disaster management and aims at the detection of messages carrying critical information for the damage assessment task. A main novelty of this study consists in the focus on out-domain and cross-event damage detection, and on the investigation of the most relevant tweet-derived features for these tasks. We devised different experiments by resorting to a wide set of linguistic features qualifying the lexical and grammatical structure of a text as well as ad-hoc features specifically implemented for this task. We investigated the most effective features that allow to achieve the best results. A further result of this study is the construction of the first manually annotated Italian corpus of social media messages for damage assessment.