We investigate the influence of nonlinear gravity corrections, arising from the Eddington-inspired Born-Infeld (EiBI) theory on wave dynamics, stability, and energy transport processes in polytropic, viscous, and turbulent solar plasmas. Analytical and numerical analyses of the Jeans-normalized quadratic dispersion relation demonstrate that both the EiBI gravity parameter $\left(\chi \right)$ and the relative polytropic sound speed $\left(\beta \right)$ independently regulate oscillation frequencies, growth rates, phase velocities, perturbation energy partitioning, and outward acoustic energy flux. Positive $\chi$ systematically elevates oscillation frequencies, phase velocities, and outward energy flux level by $\sim 10\%$ relative to the Newtonian predictions, while larger $\beta$ enhances them by up to 55%, thereby promoting wave propagation and efficient acoustic transport. Conversely, negative $\chi$ strengthens gravitational binding and increases damping rates by $\sim 40\%$, particularly for the $g$ modes. Energy partitioning analyses reveal that the EiBI corrections fundamentally restructure the kinetic-electrostatic-gravitational energy balance. While the Newtonian gravity contributes negligibly ($<4\%$), nonzero $\chi$ channels up to one-third of oscillation energy into gravitational modes. The modal surface flux calculations further confirm that only the $p$ modes drive outward energy transport (amplification for $\chi >0$, suppression for $\chi <0$). A direct comparative analysis with four years of SDO/HMI Doppler velocity observations demonstrates a robust theoretical agreement for $\chi =3\times {10}^7{\mathrm{m}}^5{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}$, providing an empirical constraint on the solar EiBI gravity through helioseismology. These findings establish a rigorous framework for testing modified gravity theories and for advancing our understanding about solar plasma stability, helioseismic signatures, and ambient atmospheric energy transport processes.

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• Space & astrophysical plasma