The rising incidence of drug overdoses (DOD) has become a global public health crisis, marked by unprecedented opioid fatalities and substance abuse deaths. Traditional surveillance systems rely on official records and healthcare data, but their inherent delays and underreporting hinder timely interventions and obscure evolving trends. In contrast, social media platforms generate vast real-time user content on DOD, reflecting genuine experiences, sentiments, and behaviors linked to substance use. To harness this wealth of information, we propose a multi-task deep learning framework, Masera, for detecting DOD-related content on social media. Masera utilizes a model-level multi-task classification approach, leveraging Mamba, a state-space model, to analyze multiple facets of DOD-related information (e.g., sentiment, lexicon). Experiments demonstrate that Masera outperforms existing detection methods in both effectiveness and robustness. This study advances public health surveillance, social media monitoring, and intervention strategies, offering a novel application of AI in addressing societal issues.