The instantaneous normal mode (INM) approach, which extends the normal mode description of collective excitations in solids to liquids, is applied to strongly coupled, three-dimensional Yukawa liquids. Based on data from Langevin dynamics simulations, we compute the instantaneous normal modes across a wide range of coupling and screening parameters. Yukawa liquids at weak to moderate screening exhibit a pronounced maximum in the INM density of states, which disappears as the coupling decreases or screening becomes stronger. The fraction of unstable modes displays a quasi-universal behavior, which can be described to a large extent by an effective coupling strength. The relation of the INM approach to the quasi-localized charge approximation (QLCA) is explored in some detail. In particular, the QLCA dispersion relation can be recovered explicitly from an appropriately weighted mode spectrum.