We investigate the formation and transport behaviors of photo-excited carriers in two dimensional transition metal dichalcogenide MoS2 under intense polarized continuous-wave excitation. By opto-electrical measurement and contactless terahertz time-domain spectroscopy, involving a dc electric field and a weak broadband terahertz as probe fields, respectively, we characterize the material's electrical and photo-responses. Circularly polarized light plays an important role in studying the valley-specific behaviors by breaking time reversal symmetry and creating a net valley polarization. In the THz TDS approach, we obtained important parameters like carrier concentrations, and carrier scattering times through fitting with a modified Drude model. Especially, the formation of negatively charged trion, a quasiparticle consisting of two electrons and one hole in MoS2, and the steady-state electron-trion dynamics made significant contributions to the material photoconductivities in the THz regime. On the other hand, under a dc electric probe field, where the trion and exciton formations are suppressed, we look at the valley Hall effect. This anomalous Hall voltage is a result of the intrinsic strong spin-orbit coupling and the lack of inversion symmetry in 2D MoS2, in addition to time reversal breaking. The valley Hall effect and its corresponding photo-conductivities can be quantitatively explained by the quantum kinetic Liouville equation, using the massive Dirac Hamiltonian model of MoS2. The analytical expressions for the longitudinal and Hall conductivity are obtained by the density matrix approach underrotating wave approximation. A good understanding of carrier formation and transport parameters are instrumental for the development of TMD-based optoelectronics, spin- and valley-tronics in the future.