In quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) are believed to provide necessary radial transport to prevent occurrence of large edge localized modes. A systematic modeling study is performed here on the low-n EHOs in a DIII-D QH-mode plasma [Chen et al. 2016 Nucl. Fusion 56 076011], by utilizing the MARS-Q code [Liu et al. 2013 Phys. Plasmas 20 042503]. Both the n = 1 and n = 2 instabilities are found to be strongly localized near the plasma edge, exhibiting the edge-peeling characteristics. The DIII-D resistive wall is found to have minor effects on these instabilities. The plasma resistivity is found to strongly modify the mode growth rate. Assuming the Spitzer model for the plasma resistivity, the computed mode growth rate scales as S^-1/3 with S being the Lundquist number. Toroidal flow of the plasma slightly stabilizes these edge localized kink-peeling modes. Drift kinetic effects all have a destabilization effect on these modes. Non-perturbative MHD-kinetic hybrid computations find that the drift kinetic effects associated with thermal particle species push the peak location of the eigenmode radially inward but still in the pedestal region. The modeled plasma temperature and density fluctuations in the plasma edge region, as well as the poloidal magnetic field perturbations along both the low and high field sides of the plasma surface, are in good agreement with experimental measurements. Finally, the quasi-linear initial value simulations find a strong non-linear interplay between the kink-peeling instability and the toroidal flow near the plasma edge. The combined effect of the damping of the flow amplitude and change of the edge flow shear is found to be the stabilizing factor for the kink-peeling mode, leading to the mode saturation and thus EHOs.