Impulsive light excitation presents a powerful tool for investigating the interdependent structural and electronic responses in layered two-dimensional (2D) halide perovskites. However, detailed understanding of the nonlinear lattice dynamics in these soft hybrid materials remains limited. Here, we explicate the intrinsic strain propagation mechanisms in 2D perovskite single crystals using transient reflection spectroscopy. Ultrafast photoexcitation leads to the generation of strain pulses via thermoelastic (TE) stress and deformation potential (DP) interaction whence their detection proceed via Brillouin scattering. Using a two-temperature model together with strain wave propagation, we discern the TE and DP contributions in strain generation. Hot carrier cooling plays a dominant role in effecting the weak modulation amplitude. Out-of-plane lattice stiffness is reduced by the weak van der Waals bond between organic layers, resulting in a slow strain propagation velocity. Our findings inject fresh insights into the basic strain properties of layered perovskites critical for manipulating their functional properties for new applications.