We present our ALMA multi-transition molecular line observational results for the ultraluminous infrared galaxy IRAS 20551−4250, which is known to contain a luminous buried active galactic nucleus and shows detectable vibrationally excited (v2 = 1f) HCN and HNC emission lines. The rotational J = 1-0, 4-3, and 8-7 of HCN, , and HNC emission lines were clearly detected at a vibrational ground level (v = 0). Vibrationally excited (v2 = 1f) J = 4-3 emission lines were detected for HCN and HNC, but not for . Their observed flux ratios further support our previously obtained suggestion, based on J = 3-2 data, that (1) infrared radiative pumping plays a role in rotational excitation at v = 0, at least for HCN and HNC, and (2) HCN abundance is higher than and HNC. The flux measurements of the isotopologue H13CN, , and HN13C J = 3-2 emission lines support the higher HCN abundance scenario. Based on modeling with collisional excitation, we constrain the physical properties of these line-emitting molecular gases, but find that higher HNC rotational excitation than HCN and is difficult to explain, due to the higher effective critical density of HNC. We consider the effects of infrared radiative pumping using the available 5-30 m infrared spectrum and find that our observational results are well-explained if the radiation source is located at 30-100 pc from the molecular gas. The simultaneously covered very bright CO J = 3-2 emission line displays a broad emission wing, which we interpret as being due to molecular outflow activity with the estimated rate of .