A new class of hitherto unexplored 1, 3, 4-oxadiazoles, OXA2a and OXA2b has been synthesized in excellent yields and characterized by IR, NMR and mass spectroscopic studies. Further, the compounds have also been identified clearly with the aid of single crystal X-ray diffraction analysis. In the crystal structure, there is a short intramolecular CH•••O contact forming S(5) ring motif in OXA2a and OXA2b. The crystal packing of OXA2a is stabilized by the CH•••π intermolecular interactions and in the crystal packing of OXA2b, the adjacent molecules are linked via CH•••N intermolecular hydrogen bonds. The intercontacts in the crystal structure are investigated through computational method using Hirshfeld surfaces. In addition, the structure and reactivity of the oxadiazole compounds have been analysed through DFT calculations. Further, both the compounds displayed strong binding affinity with targeted COX-2 enzyme which has been recognized via molecular docking study.