This paper reports measurements of processes: e+e-→γKS0K±π∓, e+e-→γK+K-π0, e+e-→γϕη, and e+e-→γϕπ0. The initial-state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to ≈4.6 GeV. The overall size of the data sample analyzed is 232 fb-1, collected by the BABAR detector running at the PEP-II e+e- storage ring. From the Dalitz plot analysis of the KS0K±π∓ final state, moduli, and relative phase of the isoscalar and the isovector components of the e+e-→KK*(892) cross section are determined. Parameters of ϕ and ρ recurrences are also measured, using a global fitting procedure which exploits the interconnection among amplitudes, moduli, and phases of the e+e-→KS0K±π∓, K+K-π0, ϕη final states. The cross section for the OZI-forbidden process e+e-→ϕπ0, and the J/ψ branching fractions to KK*(892) and K+K-η are also measured.