  The sensitive dependence of electronic and thermoelectric properties of
MoS$_2$ on the applied strain opens up a variety of applications in the
emerging area of straintronics. Using first principles based density functional
theory calculations, we show that the band gap of few layers of MoS$_2$ can be
tuned by applying i) normal compressive (NC), ii) biaxial compressive (BC), and
iii) biaxial tensile (BT) strain. A reversible semiconductor to metal
transition (S-M transition) is observed under all three types of strain. In the
case of NC strain, the threshold strain at which S-M transition occurs
increases with increasing number of layers and becomes maximum for the bulk. On
the other hand, the threshold strain for S-M transition in both BC and BT
strain decreases with the increase in number of layers. The difference in the
mechanisms for the S-M transition is explained for different types of applied
strain. Furthermore, the effect of strain type and number of layers on the
transport properties are also studied using Botzmann transport theory. We
optimize the transport properties as a function of number of layers and applied
strain. 3L- and 2L-MoS$_2$ emerge as the most efficient thermoelectric material
under NC and BT strain, respectively. The calculated thermopower is large and
comparable to some of the best thermoelectric materials. A comparison between
the feasibility of these three types of strain is also discussed.
