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We report a mechanism of massive augmentations in energy harvesting capabilities of nanofluidic devices, through the combined deployment of viscoelastic fluids and oscillatory driving pressure forces. Our analyses demonstrate that when the forcing frequency of a pressure-driven flow matches with the inverse of the relaxation time scale of a typical viscoelastic fluid, the energy conversion efficiency may get giantly amplified because of a complex interplay between the fluid rheology and ionic transport within the electrical double layer, which may open up the realm of highly efficient operating regimes of electro-hydrodynamic energy conversion in nanofluidic devices of practical relevance.