Due to the expansion of Internet and Web 2.0 phenomenon, there is a growing interest in sentiment analysis of freely opinionated text. In this paper, we propose a novel cross-source cross-domain sentiment classification, in which cross-domain-labeled Web sources (Amazon and Tripadvisor) are used to train supervised learning models (including two deep learning algorithms) that are tested on typically nonlabeled social media reviews (Facebook and Twitter). We explored a three-step methodology, in which distinct balanced training, text preprocessing and machine learning methods were tested, using two languages: English and Italian. The best results were achieved using undersampling training and a Convolutional Neural Network. Interesting cross-source classification performances were achieved, in particular when using Amazon and Tripadvisor reviews to train a model that is tested on Facebook data for both English and Italian.