This paper reports measurements of processes: e+e- →γKS0K±π, e+e-→γK+K-π0, e+e-→γ η, and e+e-→γ π0. The initial-state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to ≈4.6GeV. The overall size of the data sample analyzed is 232fb-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 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, η final states. The cross section for the OZI-forbidden process e+e-→ π0, and the J/ψ branching fractions to KK*(892) and K+K-η are also measured. © 2008 The American Physical Society.