Strange hadron transverse momentum spectra are analyzed in symmetric pp and PbPb and asymmetric pPb collision systems for their dependence on rapidity and event charged-particle multiplicity. The thermodynamically consistent Tsallis models with and without flow velocity are used to reproduce the experimental data, extracting the freeze-out parameters to gain insights into the underlying physics of the collision processes by looking into the parameters change with different multiplicities, particle types, and collision geometries. We found that with an increase in the event multiplicity, the average transverse flow velocity, effective, and kinetic freezeout temperatures increase, with heavier strange particle species exhibiting a more significant increase. The value of the non-extensivity parameter decreases with an increase in the multiplicity of the particles. For heavier particles, larger Teff and T0 and smaller q have been observed, confirming the quick thermalization and equilibrium for massive particles. Furthermore, the differences in parameter values for particle species are more significant in pp and pPb collisions than in PbPb collisions. In addition, in symmetric pp and PbPb collisions, parameter values (q,T0,βT) show more significant shifts for heavier particles compared to the lighter ones. In contrast, in asymmetric pPb collisions, both heavier and lighter particles display uniform linear progression.