Background: For many years, quasifree scattering reactions in direct kinematics have been extensively used to study the structure of stable nuclei, demonstrating the potential of this approach. The RB3 collaboration has performed a pilot experiment to study quasifree scattering reactions in inverse kinematics for a stable C12 beam. The results from that experiment constitute the first quasifree scattering results in inverse and complete kinematics. This technique has lately been extended to exotic beams to investigate the evolution of shell structure, which has attracted much interest due to changes in shell structure if the number of protons or neutrons is varied. Purpose: In this work we investigate for the first time the quasifree scattering reactions (p,pn) and (p,2p) simultaneously for the same projectile in inverse and complete kinematics for radioactive beams with the aim to study the evolution of single-particle properties from N=14 to N=15. Method: The structure of the projectiles O23, O22, and N21 has been studied simultaneously via (p,pn) and (p,2p) quasifree knockout reactions in complete inverse kinematics, allowing the investigation of proton and neutron structure at the same time. The experimental data were collected at the R3B-LAND setup at GSI at beam energies of around 400 MeV/u. Two key observables have been studied to shed light on the structure of those nuclei: the inclusive cross sections and the corresponding momentum distributions. Conclusions: The knockout reactions (p,pn) and (p,2p) with radioactive beams in inverse kinematics have provided important and complementary information for the study of shell evolution and structure. For the (p,pn) channels, indications of a change in the structure of these nuclei moving from N=14 to N=15 have been observed, i.e., from the 0d5/2 shell to the 1s1/2. This supports previous observations of a subshell closure at N=14 for neutron-rich oxygen isotopes and its weakening for the nitrogen isotopes.