Increased access to mobile devices motivates the need to design communicative visualizations that are responsive to varying screen sizes. However, relatively little design guidance or tooling is currently available to authors. We contribute a detailed characterization of responsive visualization strategies in communication-oriented visualizations, identifying 76 total strategies by analyzing 378 pairs of large screen (LS) and small screen (SS) visualizations from online articles and reports. Our analysis distinguishes between the Targets of responsive visualization, referring to what elements of a design are changed and Actions representing how targets are changed. We identify key trade-offs related to authors' need to maintain graphical density, referring to the amount of information per pixel, while also maintaining the "message" or intended takeaways for users of a visualization. We discuss implications of our findings for future visualization tool design to support responsive transformation of visualization designs, including requirements for automated recommenders for communication-oriented responsive visualizations.