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We report the results of Atacama Large Millimeter/submillimeter Array (ALMA) 1-2 kpc resolution, three rotational transition-line (J = 2-1, J = 3-2, and J = 4-3) observations of multiple dense molecular gas tracers (HCN, HCO⁺, and HNC) for 10 nearby (ultra)luminous infrared galaxies ((U)LIRGs). Following the matching of beam sizes to 1-2 kpc for each (U)LIRG, the high-J-to-low-J transition-line flux ratios of each molecule and the emission-line flux ratios of different molecules at each J transition are derived. We conduct RADEX non-LTE model calculations and find that, under a wide range of gas density and kinetic temperature, the observed HCN-to-HCO⁺ flux ratios in the overall (U)LIRGs are naturally reproduced with enhanced HCN abundance compared to HCO⁺. Thereafter, molecular gas properties are constrained primarily through the use of HCN and HCO⁺ data and the adoption of fiducial values for the HCO⁺ column density and HCN-to-HCO⁺ abundance ratio. We quantitatively confirm the following: (i) molecular gas at the (U)LIRGs' nuclei is dense (≳10^3–4 cm^–3) and warm (≳100 K), (ii) the molecular gas density and temperature in nine ULIRGs' nuclei are significantly higher than those of one LIRG's nucleus, (iii) molecular gas in starburst-dominated sources tends to be less dense and cooler than ULIRGs with luminous AGN signatures. For six selected sources, we also apply a Bayesian approach by freeing all parameters and support the above main results. Our ALMA 1-2 kpc resolution, multiple transition-line data of multiple molecules are a very powerful tool for scrutinizing the properties of molecular gas concentrated around luminous energy sources in nearby (U)LIRGs' nuclei.