With the study of Janus monolayer transition metal dichalcogenides, in which one of the two chalcogen layers is replaced by another type of chalcogen atom, research on two-dimensional materials is advancing into new areas. Yet only little is known about this new kind of material class, mainly due to the difficult synthesis. In this work, we synthesize MoSSe monolayers from exfoliated samples and compare their Raman signatures with density functional theory calculations of phonon modes that depend in a nontrivial way on doping and strain. With this as a tool, we can infer limits for the possible combinations of strain and doping levels. This reference data can be applied to all MoSSe Janus samples in order to quickly estimate their strain and doping, providing a reliable tool for future work. In order to narrow down the results for our samples further, we analyze the temperature-dependent photoluminescence spectra and time-correlated single-photon counting measurements. The lifetime of Janus MoSSe monolayers exhibits two decay processes with an average total lifetime of 1.57 ns. Moreover, we find a strong trion contribution to the photoluminescence spectra at low temperature which we attribute to excess charge carriers, corroborating our ab initio calculations.