Double perovskite oxide semiconductors possess advantageous properties such as straight bandgaps and tetragonal symmetry, which make them promising candidates for enhancing the performance of visible and ultraviolet laser diodes and LEDs. This study employs first-principles calculations to investigate the optoelectronic, thermoelectric and elastic properties of two Ba-based double perovskite oxides, namely Ba2CaMoO6 and Ba2RaMoO6. Extensive investigations have been conducted on the structural, mechanical, optoelectronic, thermoelectric and elastic properties of the compound in its ground state. Our spin-polarized computed electronic band structure calculations confirm that both compounds exhibit a nonmagnetic ground state and direct bandgap semiconducting behavior. A comprehensive optical investigation was conducted to analyze the potential utilization of these compounds in optoelectronics. The results for absorption coefficients indicate significant absorption in the ultraviolet range for both compounds. This suggests that these compounds could be utilized in various UV applications, including UV sensors, sunglasses, colored filters, and dyes. We have conducted additional tests on the thermoelectric performance of these compounds due to their intriguing computed electronic properties. Based on our calculations, the compounds Ba2CaMoO6 (ZT = 0.9973) and Ba2RaMoO6 (ZT = 1.08), which are used for long-term predictions, indicate that ZT levels are expected to increase despite a gradual and consistent decrease. The findings indicate that these configurations are useful in thermoelectric applications. As anticipated, our thorough examination revealed that these Ba2XMoO6 (X = Ca, Ra) compounds have considerable potential in optoelectronics and thermoelectricity.