Within the framework of the effective Lagrangian approach, we perform a thorough analysis of the $J/psi to Pgamma(gamma^*)$, $J/psi to VP$, $Vto Pgamma(gamma^*)$, $Pto Vgamma(gamma^*)$ and $Ptogammagamma(gamma^*)$ processes, where $V$ stand for light
vector resonances, $P$ stand for light pseudoscalar mesons, and $gamma^*$ subsequently decays into lepton pairs. The processes with light pseudoscalar mesons $eta$ and $eta$ are paid special attention to and the two-mixing-angle scheme is employed to describe their mixing. The four mixing parameters both in singlet-octet and quark-flavor bases are updated in this work. We confirm that the $J/psi to eta(eta^{prime})gamma^{(*)}$ processes are predominantly dominated by the $J/psito eta_c gamma^{*} to eta(eta^{prime})gamma^{(*)}$ mechanism. Predictions for the $J/psi to P mu^+mu^-$ are presented. A detailed discussion on the interplay between electromagnetic and strong transitions in the $J/psi to VP$ decays is given.
