Abstract We perform a systematic X-ray spectroscopic analysis of 57 local luminous and ultraluminous infrared galaxy systems (containing 84 individual galaxies) observed with the Nuclear Spectroscopic Telescope Array and/or Swift/BAT. Combining soft X-ray data obtained with Chandra, XMM-Newton, Suzaku, and/or Swift/XRT, we identify 40 hard (>10 keV) X-ray–detected active galactic nuclei (AGNs) and constrain their torus parameters with the X-ray clumpy torus model XCLUMPY. Among the AGNs at z < 0.03, for which sample biases are minimized, the fraction of Compton-thick ( N H ≥ 10 24 cm −2 ) AGNs reaches 64 − 15 + 14 % (6/9 sources) in late mergers, while it is 24 − 10 + 12 % (3/14 sources) in early mergers, consistent with the tendency reported by Ricci et al. We find that the bolometric AGN luminosities derived from the infrared data increase but the X-ray to bolometric luminosity ratios decrease with merger stage. The X-ray-weak AGNs in late mergers ubiquitously show massive outflows at subparsec to kiloparsec scales. Among them, the most luminous AGNs ( L bol,AGN ∼ 10 46 erg s −1 ) have relatively small column densities of ≲10 23 cm −2 and almost super-Eddington ratios ( λ Edd ∼ 1.0). Their torus covering factors ( C T (22) ∼ 0.6) are larger than those of Swift/BAT-selected AGNs with similarly high Eddington ratios. These results suggest a scenario where, in the final stage of mergers, multiphase strong outflows are produced due to chaotic quasi-spherical inflows, and the AGN becomes extremely X-ray weak and deeply buried due to obscuration by inflowing and/or outflowing material.