Two-particle correlations are presented for K-S(0), Lambda, and (Lambda) over bar strange hadrons as a function of relative momentum in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The dataset corresponds to an integrated luminosity of 0.607 nb(-1) and was collected using the CMS detector at the CERN LHC. These correlations are sensitive to quantum statistics and to final-state interactions between the particles. The source size extracted from the (KSKS0)-K-0 correlations is found to decrease from 4.6 to 1.6 fm in going from central to peripheral collisions. Strong interaction scattering parameters (i.e., scattering length and effective range) are determined from the Lambda K-S(0) and Lambda Lambda (including their charge conjugates) correlations using the Lednicky-Lyuboshitz model and are compared to theoretical and other experimental results.