Social media is often the first place where communities discuss the latest societal trends. Prior works have utilized this platform to extract epidemic-related information (e.g. infections, preventive measures) to provide early warnings for epidemic prediction. However, these works only focused on English posts, while epidemics can occur anywhere in the world, and early discussions are often in the local, non-English languages. In this work, we introduce the first multilingual Event Extraction (EE) framework SPEED++ for extracting epidemic event information for a wide range of diseases and languages. To this end, we extend a previous epidemic ontology with 20 argument roles; and curate our multilingual EE dataset SPEED++ comprising 5.1K tweets in four languages for four diseases. Annotating data in every language is infeasible; thus we develop zero-shot cross-lingual cross-disease models (i.e., training only on English COVID data) utilizing multilingual pre-training and show their efficacy in extracting epidemic-related events for 65 diverse languages across different diseases. Experiments demonstrate that our framework can provide epidemic warnings for COVID-19 in its earliest stages in Dec 2019 (3 weeks before global discussions) from Chinese Weibo posts without any training in Chinese. Furthermore, we exploit our framework's argument extraction capabilities to aggregate community epidemic discussions like symptoms and cure measures, aiding misinformation detection and public attention monitoring. Overall, we lay a strong foundation for multilingual epidemic preparedness.