Modeling online discourse dynamics is a core activity in understanding the spread of information, both offline and online, and emergent online behavior. There is currently a disconnect between the practitioners of online social media analysis -- usually social, political and communication scientists -- and the accessibility to tools capable of examining online discussions of users. Here we present evently, a tool for modeling online reshare cascades, and particularly retweet cascades, using self-exciting processes. It provides a comprehensive set of functionalities for processing raw data from Twitter public APIs, modeling the temporal dynamics of processed retweet cascades and characterizing online users with a wide range of diffusion measures. This tool is designed for researchers with a wide range of computer expertise, and it includes tutorials and detailed documentation. We illustrate the usage of evently with an end-to-end analysis of online user behavior on a topical dataset relating to COVID-19. We show that, by characterizing users solely based on how their content spreads online, we can disentangle influential users and online bots.