The onset of double-diffusive convection in a non-Newtonian nanofluid-saturated porous layer is investigated under the effect of internal heating and various boundary conditions. A non-Newtonian nanofluid is modeled using the Buongiorno framework for nanoparticles combined with the Jeffrey model for viscoelastic fluid behavior. The governing coupled differential equations are reduced to ordinary linear differential equations via the normal mode method, the Boussinesq approximation, and linear stability analysis. Eigenvalue problems are solved using realistic boundary conditions to determine the stationary Rayleigh numbers, which describe the initiation of non-oscillatory convection in terms of non-dimensional controlling parameters. This work is motivated by practical applications in geophysics, energy engineering, and materials science, where non-Newtonian nanofluids in porous layers are subjected to internal heating, such as in geothermal reservoirs, enhanced oil recovery, and thermal management systems. The analysis demonstrates that reduced particle density and internal heating promote convection, whereas porosity, solutal Rayleigh number, concentration Rayleigh number, and modified diffusivity ratio stabilize the system. Furthermore, reduced particle density enhances instability, while the Jeffrey parameter introduces viscoelastic effects that weaken stability without altering convection cell size. These findings provide new insights into the stabilization and destabilization mechanisms of nanofluid systems, with implications for designing advanced energy and material processing technologies.