Bilateral knee osteoarthritis (OA) poses significant challenges to individuals’ functional abilities, including quadriceps strength, postural stability, and pain perception. Understanding the complex relationships among these factors is crucial for enhancing knee OA management strategies. The primary objective of this research is to evaluate and draw comparisons between the strength of the quadriceps and the level of postural stability in two distinct groups: individuals afflicted with bilateral knee OA and those who are healthy. Furthermore, the study seeks to examine the potential correlation between the strength of the quadriceps and the level of postural stability in individuals with knee OA. In addition to this, an investigation into the potential mediating effect of pain on the relationship between these physiological factors will also be conducted. A total of 95 participants with bilateral knee OA and 95 healthy controls were recruited. Quadriceps strength was assessed using dynamometry and postural stability was evaluated through anterior–posterior and medial–lateral sway measurements along with the ellipse area using a force plate. Pain levels were measured using the Visual Analog Scale (VAS). Mediation analysis was employed to explore the role of pain in mediating the relationship between quadriceps strength and postural stability. Statistical analyses included t-tests, Pearson correlation coefficients, and mediation analysis. Knee OA participants exhibited significantly lower quadriceps strength (1.08 Nm/kg ± 0.54) compared to controls (1.54 Nm/kg ± 0.57, p < 0.001). They also demonstrated compromised postural stability with increased anterior–posterior sway (9.86 mm ± 3.017 vs. 2.98 mm ± 1.12, p < 0.001), medial–lateral sway (7.87 mm ± 2.23 vs. 3.12 mm ± 1.34, p < 0.001), and larger ellipse area (935.75 mm2 ± 172.56 vs. 436.19 mm2 ± 135.48, p < 0.001). Negative correlations were observed between quadriceps strength and postural stability variables (r = from −0.43 to −0.51, p < 0.001). Pain significantly mediated the relationship between quadriceps strength and postural stability variables (p < 0.05). This study highlights the associations between quadriceps strength, postural stability, and pain mediation in individuals with bilateral knee OA. Our findings emphasize the need for targeted interventions addressing quadriceps weakness and compromised postural stability. Additionally, the mediation effect of pain underscores the complexity of these relationships, offering insights for more effective management strategies.