Utilizing quantum second-order nonlinear transport for practical junction-free devices require materials with large and tunable nonlinearites at room temperature – a current materials platform challenge. Here, we report the nonlinear Hall effect (NLHE) in double-ionic gated bilayer graphene devices that enable unusually strong inversion breaking. We observe NLHE that are readily switchable (on, off, and sign reversed) with second order nonlinear susceptibilities χ⁽²⁾_yxx that reaches giant room-temperature values of 3 10⁻³ μm S/V, comparable to values commonly observed at low temperature in WTe₂ or in graphene-based moiré superlattices, and three-to-four orders of magnitude larger than values reported in material systems recently employed in search of a room-temperature NLHE. Our devices produce corresponding THz voltage responsivities ≃ 4 10⁴ V/W, comparable to commercially available Schottky diodes. These are orders of magnitude better than for previously reported room-temperature NLHE devices rendering double-ionic gated bilayer graphene a choice platform for junction-free nonlinear technology.