The conditional averaging technique is applied to quasi-streamwise vortices in order to clarify the impact of their structural modification on the resultant drag reduction effect in a turbulent channel flowsubjected to spanwise harmonicwall oscillation. The quantitative contributions of quadrant Reynolds shear stresses induced by the quasistreamwise vortices are calculated on the basis of the Fukagata-Iwamoto-Kasagi identity [K. Fukagata, K. Iwamoto, and N. Kasagi, "Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows," Phys. Fluids 14, L73 (2002)]. It is found that the Q2 event characterized by upwelling of low-speed fluid away from the wall governs the skin friction drag reduction at relatively small oscillation periods, whereas the Q4 event characterized by downwelling of high speed fluid toward the wall slightly contributes to drag reduction at small oscillation periods, and then to drag increase significantly with increasing the oscillation period. Detailed investigation of the conditionally averaged velocity field around the detected vortices reveals that the suppression of Q2 occurs at a certain phase when the wall motion is applied so as to oppose the rotation of near-wall streamwise vortices, whereas the enhancement of Q4 at a large oscillation period is caused by spanwise tilting of coherent structures due to the alternating spanwise shear induced by spanwise wall oscillation. Based on these findings, we develop a new predictive correlation for drag reduction effect applicable to a wide range of oscillation periods and amplitudes.