The sim-to-real gap, particularly in the inaccurate modeling of contact-rich dynamics like collisions, remains a primary obstacle to deploying robot policies trained in simulation. Conventional physics engines often trade accuracy for computational speed, leading to discrepancies that prevent direct policy transfer. To address this, we introduce Collision Learning via Augmented Sim-to-real Hybridization (CLASH), a data-efficient framework that learns a parameter-conditioned impulsive collision surrogate model and integrates it as a plug-in module within a standard simulator. CLASH first distills a base model from an imperfect simulator (MuJoCo) using large-scale simulated collisions to capture reusable physical priors. Given only a handful of real collisions (e.g., 10 samples), it then (i) performs gradient-based identification of key contact parameters and (ii) applies small-step, early-stopped fine-tuning to correct residual sim-to-real mismatches while avoiding overfitting. The resulting hybrid simulator not only achieves higher post-impact prediction accuracy but also reduces the wall-clock time of collision-heavy CMA-ES search by 42-48% compared to MuJoCo. We demonstrate that policies obtained with our hybrid simulator transfer more robustly to the real world, doubling the success rate in sequential pushing tasks with reinforcement learning and significantly increase the task performance with model-based control.