Nonlinear optical properties, such as two-(or multi-) photon absorption (2PA), are of special interest for technologically important applications in fast optical switching, in vivo imaging and so on. Highly intense infrared ultrashort pulses probe deep into samples and reveal several underlying structural perturbations (inter-layer distortions, intra-layer crumpling) and also provide information about new excited states and their relaxation. Naturally self-assembled inorganic-organic multiple quantum wells (IO-MQWs) show utility from room-temperature exciton emission features (binding energies ~200-250 meV). These Mott type excitons are highly sensitive to the self-assembly process, inorganic network distortions, thickness and inter-layer distortions of these soft two-dimensional (2D) and weak van der Waal layered hybrids. We demonstrate strong room-temperature nonlinear excitation intensity dependent two-photon absorption induced exciton photoluminescence (2PA-PL) from these IO-MQWs, excited by infrared femtosecond laser pulses. Strongly confined excitons show distinctly different one- and two-photon excited photoluminescence energies: from free-excitons (2.41 eV) coupled to the perfectly aligned MQWs and from energy down-shifted excitons (2.33 eV) that originate from the locally crumpled layered architecture. High intensity femtosecond induced PL from one-photon absorption (1PA-PL) suggests saturation of absorption and exciton-exciton annihilation, with typical reduction in PL radiative relaxation times from 270 ps to 190 ps upon increasing excitation intensities. From a wide range of IR excitation tuning, the origin of 2PA-PL excitation is suggested to arise from exciton dark states which extend below the bandgap. Observed two-photon absorption coefficients (β ~75 cm/GW) and two-photon excitation cross-sections (η2σ2 ~ 110GM), further support the evidence for 2PA excitation origin. Both 1PA- and 2PA-PL spatial mappings over large areas of single crystal platelets demonstrate the co-existence of both free and deep-level crumpled excitons with some traces of defect-induced trap state emission. We conclude that the two-photon absorption induced PL is highly sensitive to the self-assembly process of few to many mono layers, the crystal packing and deep level defects. This study paves a way to tailor the nonlinear properties of many 2D material classes. Our results thus open new avenues for exploring fundamental phenomena and novel optoelectronic applications using layered inorganic-organic and other metal organic frameworks.