Background: Obstructive sleep apnea (OSA) has been associated with adverse oral function outcomes, yet its association with oral function remains underexplored. This study aims to analyze the association between OSA and oral function problems, and whether these relationships are more pronounced among socioeconomically disadvantaged groups. Methods: Data were derived from the 2022–2023 Korea National Health and Nutrition Examination Survey (KNHANES), including 6349 participants aged 40 and above. OSA risk was assessed using the STOP-Bang questionnaire. Oral function was evaluated through chewing discomfort, speaking discomfort, and dental pain. Complex sample logistic regression was performed, adjusting for demographic, socioeconomic, and health-related covariates. Stratified analyses were conducted to examine whether the association differed across socioeconomic groups. Result: High OSA risk was significantly associated with chewing discomfort (OR: 1.365, 95% CI: 1.121–1.662), speaking discomfort (OR: 1.534, 95% CI: 1.126–2.082), and dental pain (OR: 1.198, 95% CI: 1.006–1.431). Stratified analyses showed stronger associations in low education or income groups. For instance, those in the lowest income group were over five times more likely to report speaking discomfort (OR = 5.207, 95% CI: 2.365–11.462) than those in the highest. Conclusions: OSA risk is significantly associated with impaired oral function, particularly among socioeconomically disadvantaged groups. These findings underscore the need for integrated public health approaches that address both sleep and oral health disparities.