The vibrational and electronic properties of 2-dimensinal (2D) materials can be efficiently tuned by external strain due to their good stretchability. Resonant Raman spectroscopy is a versatile tool to study the physics of phonons, electrons and their interactions simultaneously, which is particularly useful for the investigation of strain effect on 2D materials. Here, for the first time, we report the resonant Raman study of strained few-layer InSe ({\gamma}-phase). Under ~ 1% of uniaxial tensile strain, one order of magnitude enhancement of Raman intensity for longitudinal optical (LO) phonon is observed, while other modes exhibit only modest change. Further analysis demonstrates that it arises from the intraband electron-phonon scattering channel for LO phonon in resonance. The large enhancement of Raman intensity provides us a sensitive and novel method to characterize the strain effect and a mapping of the strain distribution in a wrinkled sample is demonstrated. In addition, we observed sizable redshifts of first-order optical phonon modes. The shift rate exhibits phonon mode dependence, in excellent agreement with density functional perturbation theory (DFPT) calculations. Our study paves the way for sensitive strain quantification in few-layer InSe and its application in flexible electronic and optoelectronic devices.