Current vertex correction (CVC), the back-flow-like correction to the current, comes from conservation laws, and the CVC due to electron correlation contains information about many-body effects. However, it has been little understood how the CVC due to electron correlation affects the charge transports of a correlated multiorbital system. To improve this situation, I studied the inplane resistivity, ρ ab , and the Hall coefficient in the weak-field limit, RH, in addition to the magnetic properties and the electronic structure, for a t2g-orbital Hubbard model on a square lattice in a paramagnetic state away from or near an antiferromagnetic (AF) quantum-critical point (QCP) in the fluctuation-exchange (FLEX) approximation with the CVCs arising from the self-energy (Σ), the Maki-Thompson (MT) irreducible four-point vertex function, and the main terms of the AslamasovLarkin (AL) one. Then, I found three main results about the CVCs. First, the main terms of the AL CVC does not qualitatively change the results obtained in the FLEX approximation with the Σ CVC and the MT CVC. Second, ρ ab and RH near the AF QCP have high-temperature region, governed mainly by the Σ CVC, and low-temperature region, governed mainly by the Σ CVC and the MT CVC. Third, in case away from the AF QCP, the MT CVC leads to a considerable effect on only RH at low temperatures, although RH at high temperatures and ρ ab at all temperatures considered are sufficiently described by including only the Σ CVC. Those findings reveal several aspects of many-body effects on the charge transports of a correlated multiorbital system. I also achieved the qualitative agreement with several experiments of Sr2RuO4 or Sr2Ru0.975Ti0.025O4. Moreover, I showed several better points of this theory than other theories.