We present the results of an elliptic flow, v2, analysis of Cu+Cu collisions recorded with the solenoidal tracker detector (STAR) at the BNL Relativistic Heavy Ion Collider at √sNN=62.4 and 200 GeV. Elliptic flow as a function of transverse momentum, v2(pT), is reported for different collision centralities for charged hadrons h± and strangeness-ontaining hadrons K0S, Λ, Ξ, and ϕ in the midrapidity region |η|<1.0. Significant reduction in systematic uncertainty of the measurement due to nonflow effects has been achieved by correlating particles at midrapidity, |η|<1.0, with those at forward rapidity, 2.5<|η|<4.0. We also present azimuthal correlations in p+p collisions at √s=200 GeV to help in estimating nonflow effects. To study the system-size dependence of elliptic flow, we present a detailed comparison with previously published results from Au+Au collisions at √sNN=200 GeV. We observe that v2(pT) of strange hadrons has similar scaling properties as were first observed in Au+Au collisions, that is, (i) at low transverse momenta, pT<2 GeV/c, v2 scales with transverse kinetic energy, mT−m, and (ii) at intermediate pT, 2<pT<4 GeV/c, it scales with the number of constituent quarks, nq. We have found that ideal hydrodynamic calculations fail to reproduce the centrality dependence of v2(pT) for K0S and Λ. Eccentricity scaled v2 values, v2/ɛ, are larger in more central collisions, suggesting stronger collective flow develops in more central collisions. The comparison with Au+Au collisions, which go further in density, shows that v2/ɛ depends on the system size, that is, the number of participants Npart. This indicates that the ideal hydrodynamic limit is not reached in Cu+Cu collisions, presumably because the assumption of thermalization is not attained.