Three organic ligands bearing 1,2,4-triazolyl donor moieties, (S)-4-(1-phenylpropyl)-1,2,4-triazole (trethbz), 4-(1,2,4-triazol-4-yl)benzoic acid (trPhCO2H), and 3-(1H-imidazol-4-yl)-2-(1,2,4-triazol-4-yl)propionic acid (trhis), were prepared to evaluate their coordination behavior in the development of molybdenum(VI) oxide organic hybrids. Four compounds, [Mo2O6(trethbz)2]·H2O (1), [Mo4O12(trPhCO2H)2]·0.5H2O (2a), [Mo4O12(trPhCO2H)2]·H2O (2b), and [Mo8O25(trhis)2(trhisH)2]·2H2O (3), were synthesized and characterized. The monofunctional tr-ligand resulted in the formation of a zigzag chain [Mo2O6(trethbz)2] built up from cis-{MoO4N2} octahedra united through common μ2-O vertices. Employing the heterodonor ligand with tr/-CO2H functions afforded either layer or ribbon structures of corner- or edge-sharing {MoO5N} polyhedra (2a or 2b) stapled by tr-links in axial positions, whereas -CO2H groups remained uncoordinated. The presence of the im-heterocycle as an extra function in trhis facilitated formation of zwitterionic molecules with a protonated imidazolium group (imH+) and a negatively charged -CO2- group, whereas the tr-fragment was left neutral. Under the acidic hydrothermal conditions used, the organic ligand binds to molybdenum atoms either through [N-N]-tr or through both [N-N]-tr and μ2-CO2- units, which occur in protonated bidentate or zwitterionic tetradentate forms (trhisH+ and trhis, respectively). This leads to a new zigzag subtopological motif (3) of negatively charged polyoxomolybdate {Mo8O25}n2n- consisting of corner- and edge-sharing cis-{MoO4N2} and {MoO6} octahedra, while the tetradentate zwitterrionic trhis species connect these chains into a 2D net. Electronic spectra of the compounds showed optical gaps consistent with semiconducting behavior. The compounds were investigated as epoxidation catalysts via the model reactions of achiral and prochiral olefins (cis-cyclooctene and trans-β-methylstyrene) with tert-butylhydroperoxide. The best-performing catalyst (1) was explored for the epoxidation of other olefins, including biomass-derived methyl oleate, methyl linoleate, and prochiral dl-limonene.