Nanofluids play a pivotal role in the heat transport phenomenon and are essential in the cooling process of small gadgets like computer microchips and other related applications in microfluidics. Having such amazing applications of nanofluids, we intend to present a theoretical analysis of the thermally stratified 3D flow of nanofluid containing nano solid particles (Cu and Al2O3) over a nonlinear stretchable sheet with Ion and Hall slip effects. Moreover, the features of buoyance effect and non-uniform heat source/skin are also analyzed. For the study of numerically better results, Tawari and Das model is adopted here. For the conversion of the system of partial differential equations into ordinary differential equations, apposite transformations are engaged and are tackled by utilizing the bvp4c scheme of MATLAB software. The effects of dimensionless parameters on velocity and temperature profiles are depicted with the help of graphs. Additionally, the Skin friction coefficient and Nusselt number for the practical applications are examined in the tabular form. Verification of the current study by comparing it with an already published work in a special case is also a part of this study. Results show that the thermal performance of copper nanoparticles is more than alumina nanoparticles. An upsurge in the temperature of nanofluid is observed when the strength of the magnetic field is enhanced. However, the temperature of partially ionized nanofluid is significantly lowered because of the collisions of electrons and ions.