Abstract: We investigate the possibility of probing the hot and dense nuclear matter-created in relativistic heavyion collisions (HICs)-with strange vector mesons (K*, (K) over bar*). Our analysis is based on the nonequilibrium parton-hadron-string dynamics (PHSD) transport approach which incorporates partonic and hadronic degrees of freedom and describes the full dynamics of HIC on a microscopic level-starting from the primary nucleon-nucleon collisions to the formation of the strongly interacting quark gluon plasma (QGP), followed by dynamical hadronization of (anti)quarks as well as final hadronic elastic and inelastic interactions. This allows us to study the K* and (K) over bar* meson formation from the QGP as well as the in-medium effects related to the modification of their spectral properties during the propagation through the dense and hot hadronic environment in the expansion phase. We employ relativistic Breit-Wigner spectral functions for the K*, (K) over bar* mesons with self-energies obtained from a self-consistent coupled-channel G-matrix approach to study the role of in-medium effects on the K* and (K) over bar* meson dynamics in heavy-ion collisions from FAIR/NICA to LHC energies. According to our analysis most of the final K* /(K) over bar*'s, that can be observed experimentally by reconstruction of the invariant mass of pi + K((K) over bar) pairs, are produced during the late hadronic phase and originate dominantly from the K((K) over bar) + pi -> K*( (K) over bar*) formation channel. The amount of K*/ (K) over bar*'s, originating from the QGP channel is comparatively small even at LHC energies and those K* /(K) over bar*'s can hardly be reconstructed experimentally due to the rescattering of final pions and (anti)kaons. This mirrors the results from our previous study on the strange vector-meson production in heavy-ion collisions at RHIC energies. We demonstrate that K* /(K) over bar* in-medium effects should be visible at FAIR/NICA and BES RHIC energies, where the production of K* /(K) over bar*'s occurs at larger net-baryon densities. Finally, we present the experimental procedures to extract the information on the resonance masses and widths by fitting the final mass spectra at LHC energies.