Tuning physical properties of transition metal dichalcogenide (TMD) monolayers by strain engineering have most widely studied, and recently Janus TMD monolayer MoSSe has been synthesized. In this work, we systematically study biaxial strain dependence of electronic structures and transport properties of Janus TMD MXY (M = Mo or W, X/Y = S, Se, or Te) monolayer by using generalized gradient approximation (GGA) plus spin-orbit coupling (SOC). It is found that SOC has a noteworthy detrimental influence on power factor in p-type MoSSe, WSSe, n-type WSTe, p-type MoSeTe and WSeTe, and has a negligible influence on one in n-type MoSSe, MoSTe, p-type WSTe and n-type MoSeTe. These can be understood by considering SOC effects on their valence and conduction bands. For all six monolayers, the energy band gap firstly increases, and then decreases, when strain changes from compressive one to tensile one. It is found that strain can tune strength of bands convergence of both valence and conduction bands by changing the numbers and relative position of valence band extrema (VBE) or conduction band extrema (CBE), which can produce very important effects on their electronic transport properties. By applying appropriate compressive or tensile strain, both n-or p-type Seebeck coefficient can be enhanced by strain-induced band convergence, and then the power factor can be improved. Our works further enrich studies on strain dependence of electronic structures and transport properties of new-style TMD monolayers, and motivate farther experimental works.