This study introduces ValueScope, a framework leveraging language models to quantify social norms and values within online communities, grounded in social science perspectives on normative structures. We employ ValueScope to dissect and analyze linguistic and stylistic expressions across 13 Reddit communities categorized under gender, politics, science, and finance. Our analysis provides a quantitative foundation showing that even closely related communities exhibit remarkably diverse norms. This diversity supports existing theories and adds a new dimension--community preference--to understanding community interactions. ValueScope not only delineates differing social norms among communities but also effectively traces their evolution and the influence of significant external events like the U.S. presidential elections and the emergence of new sub-communities. The framework thus highlights the pivotal role of social norms in shaping online interactions, presenting a substantial advance in both the theory and application of social norm studies in digital spaces.