An R and K' atlas of the IRAS 1 Jy sample of 118 ultraluminous infrared galaxies (ULIGs) was presented in a companion paper (our Paper I). The present paper discusses the results from the analysis of these images supplemented with new spectroscopic data obtained at Keck. All but one object in the 1 Jy sample show signs of a strong tidal interaction/merger. Multiple mergers involving more than two galaxies are seen in no more than five of the 118 (<5%) systems. None of the 1 Jy sources is in the first-approach stage of the interaction, and most (56%) of them harbor a single disturbed nucleus and are therefore in the later stages of a merger. Seyfert galaxies (especially those of type 1), warm ULIGs (f₂₅/f₆₀ > 0.2), and the more luminous systems (>10^12.5 L) all show a strong tendency to be advanced mergers with a single nucleus.

     The individual galaxies in the binary systems of the 1 Jy sample show a broad distribution in host magnitudes (luminosities) with a mean of -21.02 ± 0.76 mag (0.85 L*) at R and -23.98 ± 1.25 mag (0.90 L*) at K', and a R- or K'-band luminosity ratio generally less than ~4. Single-nucleus ULIGs also show a broad distribution in host magnitudes (luminosities) with an average of -21.77 ± 0.92 mag (1.69 L*) at R and -25.03 ± 0.94 mag (2.36) at K'. These distributions overlap considerably with those of quasars. The same statement applies to R-K' colors in ULIG and quasar hosts.

     An analysis of the surface brightness profiles of the host galaxies in single-nucleus sources reveals that about 73% of the R and K' surface brightness profiles are fitted adequately by an elliptical-like R^1/4 law. These elliptical-like 1 Jy systems have luminosity and R-band axial ratio distributions that are similar to those of normal (inactive) intermediate-luminosity ellipticals and follow with some scatter the same μ_e-r_e relation, giving credence to the idea that some of these objects may eventually become intermediate-luminosity elliptical galaxies if they get rid of their excess gas or transform this gas into stars. These elliptical-like hosts are most common among merger remnants with Seyfert 1 nuclei (83%), Seyfert 2 optical characteristics (69%), or mid-infrared (ISO) AGN signatures (80%). The mean half-light radius of these ULIGs is 4.80 ± 1.37 kpc at R and 3.48 ± 1.39 kpc at K', typical of intermediate-luminosity ellipticals. These values are in excellent agreement with recent quasar measurements obtained at H with the Hubble Space Telescope (HST), but they are systematically lower than other HST measurements derived at R. The reason for this discrepancy between the two quasar data sets is not known.

     In general, the results from the present study are consistent with the merger-driven evolutionary sequence "cool ULIGs→warm ULIGs→quasars." However, many exceptions appear to exist to this simple picture (e.g., 46% of the 41 advanced mergers show no obvious signs of Seyfert activity). This underlines the importance of using a large homogeneous sample like the 1 Jy sample to draw statistically meaningful conclusions; the problems of small sample size and/or inhomogeneous selection criteria have plagued many studies of luminous infrared galaxies in the past.