The sensitive dependence of the electronic and thermoelectric properties of MoS₂ on 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 a few layers of MoS₂ can be tuned by applying normal compressive (NC) strain, biaxial compressive (BC) strain, and 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 the S-M transition occurs increases when the number of layers increase and becomes maximum for the bulk. On the other hand, the threshold strain for the S-M transition in both BC and BT strains decreases when the number of layers increase. The difference in the mechanisms for the S-M transition is explained for different types of applied strain. Furthermore, the effect of both strain type and the number of layers on the transport properties are also studied using Botzmann transport theory. We optimize the transport properties as a function of the number of layers and the applied strain. 3L- and 2L-MoS₂ emerge as the most efficient thermoelectric materials under NC and BT strain, respectively. The calculated thermopower is large and comparable to some of the best thermoelectric materials. A comparison among the feasibility of these three types of strain is also discussed.