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We studied the electron and structural dynamics of the topological semimetal WTe₂ using time- and angle-resolved photoemission spectroscopy (trARPES), ultrafast electron diffraction (UED) and density functional theory (DFT). We report the observation of band oscillations at multiple frequencies due to A₁ coherent phonon modes. By isolating the effect of each phonon on the different electronic bands, we reveal the complexity of electron-phonon coupling in the electronic band structure. Combining these spectroscopic observations with UED results, we quantify the electron-phonon coupling strength in WTe₂ for two A₁ phonons and find that inter-layer modes are more weakly coupled than intra-layer modes. We explain this difference with the general expectation that Van der Waals bonds are weaker than covalent bonds. Our results impact the understanding how lattice structure determines electronic and topological properties.