We calculate the effects of finite density and temperature of isospin asymmetric strange hadronic matter, for different strangeness fractions, on the in-medium properties of vector (D*, D-s*, B*, B-s*) and axial-vector (D-1, D-1s, B-1, B-1s) mesons, using the chiral hadronic SU(3) model and QCD sum rules. We focus on the evaluation of in-medium mass-shift and shift in decay constant of above vector and axial-vector mesons. In the quantum chromodynamics sum rule approach, the properties, e.g., the masses and decay constants of vector and axial-vector mesons are written in terms of quark and gluon condensates. These quark and gluon condensates are evaluated in the present work within the chiral SU(3) model, through the medium modification of scalar-isoscalar fields sigma and., the scalar-isovector field delta, and the scalar dilaton field , in the strange hadronic medium which includes both nucleons as well as hyperons. As we shall see in detail, the masses and decay constants of heavy vector and axial-vector mesons are affected significantly from isospin asymmetry and the strangeness fraction of the medium, and these modifications may influence the experimental observables produced in heavy-ion collision experiments. The results of present investigations of in-medium properties of vector and axial-vector mesons at finite density and temperature of strange hadronic medium may be helpful for understanding the experimental data from heavy-ion collision experiments in particular for the compressed baryonic matter (CBM) experiment of the FAIR facility at GSI, Germany.