This paper delves into the practical finite-time synchronization (FTS) problem for inertial neural networks (INNs) with external disturbances. Firstly, based on Lyapunov theory, the local practical FTS of INNs with bounded external disturbances can be realized by effective finite time control. Then, building upon the local results, we extend the synchronization to a global practical level under delayed impulsive control. By designing appropriate hybrid controllers, the global practical FTS criteria of disturbed INNs are obtained and the corresponding settling time is estimated. In addition, for impulsive control, the maximum impulsive interval is used to describe the frequency at which the impulses occur. We optimize the maximum impulsive interval, aiming to minimize impulses occurrence, which directly translates to reduced control costs. Moreover, by comparing the global FTS results for INNs without external disturbances, it can be found that the existence of perturbations necessitates either higher impulsive intensity or denser impulses to maintain networks synchronization. Two examples are shown to demonstrate the reasonableness of designed hybrid controllers.