In the age of social media, where billions of internet users share information and opinions, the negative impact of pandemics is not limited to the physical world. It provokes a surge of incomplete, biased, and incorrect information, also known as an infodemic. This global infodemic jeopardizes measures to control the pandemic by creating panic, vaccine hesitancy, and fragmented social response. Platforms like Facebook allow advertisers to adapt their messaging to target different demographics and help alleviate or exacerbate the infodemic problem depending on their content. In this paper, we propose a minimally supervised multi-task learning framework for understanding messaging on Facebook related to the COVID vaccine by identifying ad themes and moral foundations. Furthermore, we perform a more nuanced thematic analysis of messaging tactics of vaccine campaigns on social media so that policymakers can make better decisions on pandemic control.