Due to the unique optical responses induced by vertical atomic asymmetry inside a monolayer, two-dimensional Janus structures have been conceived as promising building blocks for nanoscale optical devices. In this paper, second harmonic generation (SHG) in Janus transition metal chalcogenide oxide monolayers is systematically investigated by the first-principles calculations. Second-order nonlinear susceptibilities are theoretically determined for Janus MXO (M = Mo/W, X = S/Se/Te) monolayers. The calculated values are comparable in magnitude with Janus MoSSe monolayer. X-M-O symmetry breaking leads to non-zero components in vertical direction, compared with the non-Janus structure. Focusing on the SHG induced by incident light at 1064 nm, polarization-dependent responses of six Janus MXO monolayers are demonstrated. The symmetry of p-polarization changes from six-fold to three-fold with acute incidence angle. Moreover, the effects of biaxial strain on band structures and SHG are further investigated, taking MoSO as an exemplary case. We expect these results to bring in recipes for designing nonlinear optical devices based on Janus transition metal chalcogenide oxide monolayers.