The main aim of this paper is to generalize and improve our earlier results in [J. Differential Equations \textbf{317} (2022), 365-386; \textbf{367} (2023), 783-803] and our joint result with Pavel Ludv\'{\i}k in [Internat. J. Bifur.\ Chaos Appl. Sci. Engrg. \textbf{33} (2023), no.\ 9, 2350113]. The theoretical part concerns the topological entropy of nonautonomous multivalued dynamical systems, studied by means of the asymptotic Nielsen theory. The practical part deals with the application of theoretical results via the associated Poincaré translation operators to impulsive differential inclusions on tori.