Objective: The objective of the study was to evaluate how gender, socioeconomic position (SEP), race/ethnicity and nationality intersect to structure social inequalities in adult oral health among American adults. Methods: Data from adults aged 20 years or over who participated in the National Health and Nutrition Examination Survey (NHANES) 2009–2018 were analysed. The outcomes were poor self-rated oral health and edentulism among all adults (n = 24 541 and 21 446 participants, respectively) and untreated caries and periodontitis among dentate adults (n = 16 483 and 9829 participants, respectively). A multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) was conducted for each outcome, by nesting individuals within 48 intersectional strata defined as combinations of gender, SEP, race/ethnicity and nationality. Intersectional measures included the variance partition coefficient (VPC), the proportional change in variance (PCV) and predicted excess probability due to interaction. Results: Substantial social inequalities in the prevalence of oral conditions among adults were found, which were characterized by high between-stratum heterogeneity and outcome specificity. The VPCs of the simple intersectional model showed that 9.4%–12.7% of the total variance in the presentation of oral conditions was attributed to between-stratum differences. In addition, the PCVs from the simple intersectional model to the intersectional interaction model showed that 84.1%–97.1% of the stratum-level variance in the presentation of oral conditions was attributed to the additive effects of gender, SEP, race/ethnicity and nationality. The point estimates of the predictions for some intersectional strata were suggestive of an intersectional interaction effect. However, the 95% credible intervals were very wide and the estimations inconclusive. Conclusions: This analysis highlights the value of the intersectionality framework to understand heterogeneity in social inequalities in oral health. These inequalities were mainly due to the additive effect of the social identities defining the intersectional strata, with no evidence of interaction effects.