In this work, we pave the way to calculate the productions of ω and K S 0 mesons with large p T in p+p and A+A collisions both at RHIC and LHC. The fragmentation functions (FFs) of the ω meson in vacuum at next-to-leading order (NLO) are obtained by evolving the NLO DGLAP evolution equations with rescaled ω FFs at initial scale Q 0 2 = 1.5   GeV 2 from a broken SU(3) model, and the FFs of K S 0 in vacuum are taken from AKK08 parametrization directly. Within the framework of the NLO pQCD improved parton model, we arrive at good descriptions of the experimental data on ω and K S 0 in p+p both at RHIC and LHC. With the higher-twist approach, to take into account jet quenching effect by medium-modified FFs, nuclear modification factors for ω meson and K S 0 meson both at RHIC and LHC are presented with different sets of jet transport coefficients q ^ 0 . Then we make a global extraction of q ^ 0 both at RHIC and LHC by confronting our model calculations with all available data on six identified mesons: π 0 , η , ρ 0 , ϕ , ω , and K S 0 . The minimum value of total χ 2 / d . o . f for productions of these mesons gives the best value of q ^ 0 = 0.5 G e V 2 / f m for Au+Au collisions with s NN = 200  GeV at RHIC, and q ^ 0 = 1.2 G e V 2 / f m for Pb+Pb collisions with s NN = 2.76  TeV at LHC, respectively, with the QGP spacetime evolution given by the event-by-event viscous hydrodynamics model IEBE-VISHNU. With these global extracted values of q ^ 0 , nuclear modification factors of π 0 , η , ρ 0 , ϕ , ω , and K S 0 in A+A collisions are presented, and predictions of yield ratios such as ω / π 0 and K S 0 / π 0 at the high- p T regime in heavy-ion collisions both at RHIC and LHC are provided.