Semiconductor monolayer transition metal dichalcogenides (TMDs) have brought a new paradigm by introducing optically addressable valley degree of freedom. Concomitantly, their high flexibility constitutes a unique platform that links optics to mechanics via valleytronics. With the intention to expedite the research in this direction, we investigated ten TMDs, namely MoS2, MoSe2, MoTe2, WS2, WSe2, WTe2, MoSSe, MoSeTe, WSSe, and WSeTe, which particularly includes their so-called janus types (JTMDs). First, we obtained their electronic band structures using regular and hybrid density functional theory (DFT) calculations in the presence of the spin–orbit coupling and biaxial or uniaxial strain. Our DFT results indicated that against the expectations based on their reported piezoelectric behavior, JTMDs typically interpolated between the standard band properties of the constituent TMDs without producing a novel feature. Next, by fitting to our DFT data we generated both spinless and spinful k · p parameter sets which are quite accurate over the K valley where the optical activity occurs. As an important application of this parametrization, we considered the circular and linear dichroism under strain. Among the studied (J)TMDs, WTe2 stood out with its largest linear dichroism under uniaxial strain because of its narrower band gap and large K valley uniaxial deformation potential. This led us to suggest WTe2 monolayer membranes for optical polarization-based strain measurements, or conversely, as strain tunable optical polarizers.