The fast development of high-performance devices for diverse applications requires nanoscale materials with multifunctional properties, motivating theoretical exploration into novel two-dimensional (2D) materials. In this work, we propose a new family of 2D nanomaterials, Janus transition metal oxides and chalcogenides MXY (M = Ti, Zr, or Hf; X = S or Se; Y = O or S; X ≠ Y) monolayers, for their versatile applications. We find that the Janus MXY monolayers are semiconductors with a wide range of band gaps ranging from 0.739 to 2.884 eV. We show that TiSO, ZrSO, and HfSO monolayers are promising candidates for photocatalysis because of their suitable band gaps and optimal redox potentials for water splitting, and ZrSeS and HfSeS monolayers are suitable candidates for nanoscale electronics because of their high carrier mobility. We further show that TiSO, ZrSO, and ZrSeO monolayers possess large piezoelectric properties because of the broken inversion symmetry stemmed from the different atomic sizes and electronegativities of the X and Y elements, which are better or comparable to other 2D and bulk piezoelectric materials. Our study demonstrates that the 2D Janus MXYs may find versatile applications into photocatalysts, electronics, sensors, and energy harvesting/conversion.