In this manuscript, we consider a (3+1)-dimensional Sharma-Tasso-Olver-like (STOL) model, which can be used to describe dispersive wave phenomena in optics, plasmas, quantum physics, and others. Based on the simplified Hirota approach, the n-soliton solutions are obtained. We observe that the collisions are non-elastic fusion or fission phenomena where some kink waves disappear due to soliton fusion, or a single kink wave splits into more kink waves due to soliton fusion. We derive kinky-lump breather, combo line kink and kinky-lump breather, and a pair of kinky-lump breather wave solutions that degenerate from two-, three- and four-solitons respectively by choosing complex conjugate values involving free parameters. Moreover, we demonstrate a few new collisions of the Jacobi elliptic sine function with one soliton, and a periodic cosine function which provides kinky-periodic waves and double-periodic waves. All special properties of those collision solutions are illustrated with the 3D, density and contour plots. •We consider (3+1)-dimensional Sharma-Tasso-Olver-like model.•The solitons, periodic, Jacobi elliptic functions and its interactions are obtained.•We observed the interactions as non-elastic fusion or fission phenomena.•The solutions are illustrated with the 3D, density and contour plots.