The properties of strange mesons (K, K¯ and K¯∗) in dense matter are studied using a unitary approach in coupled channels for meson-baryon scattering. The kaon-nucleon interaction incorporates s- and p-wave contributions within a chiral model whereas the interaction of K¯∗ with nucleons is obtained in the framework of the local hidden gauge formalism. The in-medium solution for the scattering amplitude accounts for Pauli blocking effects, mean-field binding on baryons, and meson self-energies. We obtain the K, K¯ and K¯∗ (off-shell) spectral functions in the nuclear medium and study their behaviour at finite density, temperature and momentum. We also analyze the energy weighted sum rules of the kaon propagator as a quality test of model calculations. We finally estimate the transparency ratio of the γA→K+K∗−A′ reaction, which we propose as a feasible scenario at present facilities to detect in-medium modifications of the K¯∗ meson.