This paper presents multiplicity measurements of KS0, Λ, and Λ¯ produced in 120  GeV/c proton-carbon interactions. The measurements were made using data collected at the NA61/SHINE experiment during two different periods. Decays of these neutral hadrons impact the measured π+, π-, p and p¯ multiplicities in the 120  GeV/c proton-carbon reaction, which are crucial inputs for long-baseline neutrino experiment predictions of neutrino beam flux. The double-differential multiplicities presented here will be used to more precisely measure charged-hadron multiplicities in this reaction, and to reweight neutral hadron production in neutrino beam Monte Carlo simulations.