A large family of bifunctional 1,2,4-triazole molecular tectons (tr) has been explored for engineering molybdenum(VI) oxide hybrid solids. Specifically, tr ligands bearing auxiliary basic or acidic groups were of the type amine, pyrazole, 1H-tetrazole, and 1,2,4-triazole. The organically templated molybdenum(VI) oxide solids with the general compositions [MoO3(tr)], [Mo2O6(tr)], and [Mo2O6(tr)(H2O)2] were prepared under mild hydrothermal conditions or by refluxing in water. Their crystal structures consist of zigzag chains, ribbons, or helixes of alternating cis-{MoO4N2} or {MoO5N} polyhedra stapled by short [N-N]-tr bridges that for bitriazole ligands convert the motifs into 2D or 3D frameworks. The high thermal (235-350 °C) and chemical stability observed for the materials makes them promising for catalytic applications. The molybdenum(VI) oxide hybrids were successfully explored as versatile oxidation catalysts with tert-butyl hydroperoxide (TBHP) or aqueous H2O2 as an oxygen source, at 70 °C. Catalytic performances were influenced by the different acidic-basic properties and steric hindrances of coordinating organic ligands as well as the structural dimensionality of the hybrid.