We provide details of the study of psi(3770) non-D (D) over bar decays into VP, where V and P denote light vector meson and pseudoscalar meson, respectively. We find that the electromagnetic interaction plays little role in these processes, while the strong interaction dominates. The strong interaction can be separated into two parts, i.e., the short-distance part probing the wave function at origin and the long-distance part reflecting the soft gluon exchanged dynamics. The long-distance part is thus described by the intermediate charmed meson loops. We show that the transition of psi(3770) -> VP can be related to psi(3686) -> VP such that the parameters in our model can be constrained by comparing the different parts in psi(3770) -> VP to those in psi(3686) -> VP. Our quantitative results confirm the findings of Zhang et al. [Phys. Rev. Lett. 102, 172001 (2009)] that the OZI-rule-evading long-distance strong interaction via the intermediate meson loops plays an important role in psi(3770) decays and could be a key towards a full understanding of the mysterious psi(3770) non-D (D) over bar decay mechanism.