A study of the inclusive production of KS0, Λ, and Λ̄ in π-p interactions at 15 GeV / c is presented. Inclusive cross sections for single neutral strange particles and neutral-strange-particle pairs are given. Longitudinal- and transverse-momentum distributions of the produced particles are presented. The average charged multiplicities of the systems recoiling against the Λ and the KS0 are compared and the results analyzed in the framework of a simple model. The Λ polarization is found to be in good agreement with Λ production from other strangeness-nonannihilating processes. Production of Λ's in the target fragmentation region is studied in the framework of the triple-Regge-pole-exchange model. The cross section for inclusive K*+(890) production has been measured as 195 ± 35 μb, and the +(1385) inclusive cross section has been found to be 174 ± 25 μb. The K*+(890) and +(1385) differential cross sections as functions of rapidity and transverse momentum are presented and discussed.