The PHENIX experiment at the Relativistic Heavy Ion Collider has performed a systematic study of K-S(0) and K*(0) meson production at midrapidity in p + p, d + Au, and Cu + Cu collisions at root s(NN) = 200 GeV. The K-S(0) and K*(0) mesons are reconstructed via their K-S(0) -> pi(0)(-> gamma gamma) pi(0)(-> gamma gamma) and K*(0) -> K-+/-pi(-/+) decay modes, respectively. The measured transverse-momentum spectra are used to determine the nuclear modification factor of K-S(0) and K*(0) mesons in d + Au and Cu + Cu collisions at different centralities. In the d + Au collisions, the nuclear modification factor of K-S(0) and K*(0) mesons is almost constant as a function of transverse momentum and is consistent with unity, showing that cold-nuclear-matter effects do not play a significant role in the measured kinematic range. In Cu + Cu collisions, within the uncertainties no nuclear modification is registered in peripheral collisions. In central collisions, both mesons show suppression relative to the expectations from the p + p yield scaled by the number of binary nucleon-nucleon collisions in the Cu + Cu system. In the p(T) range 2-5 GeV/c, the strange mesons (K-S(0), K*(0)) similarly to the phi meson with hidden strangeness, show an intermediate suppression between the more suppressed light quark mesons (pi(0)) and the nonsuppressed baryons (p, (p) over bar). At higher transverse momentum, p(T) > 5 GeV/c, production of all particles is similarly suppressed by a factor of approximate to 2.