We present measurements of strange hadron (, , and Ξ++Ξ−) transverse momentum (pT) spectra in pp, pPb, and PbPb collisions over a wide range in charge-particle multiplicity and particle rapidity. The data were taken with the CMS detector at the LHC for pp collisions at , pPb collisions at , and PbPb collisions at . We find the average transverse kinetic energy (KET) increases with event multiplicity, with a faster rate for heavier particle species. At similar multiplicities, we observe the separation in the 〈KET〉, which is defined as 〈KET〉=〈mT〉−m, where , between different particle species is larger for pp and pPb systems than PbPb system. In pPb collisions, 〈KET〉 is found to be larger in the Pb-going direction than in the p-going direction. This trend of asymmetry becomes more evident for heavier particle species as event multiplicity increases. We also compare the data to models motivated by hydrodynamics.