We present new interferometric H I and optical observations of three amorphous galaxies, systems with a smooth, high surface brightness but an asymmetrical distribution of light. All three galaxies are forming stars and have LMC-like emission-line ratios, low dust content, and high H I velocity dispersions. NGC 1140 has a boxy inner morphology with a hook off one corner. At low light levels unusual extensions of starlight are seen curving to the northwest and southeast. The galaxy contains a very luminous central star-forming region and a small chain of H II regions that coincide with the hook. The central H II region has broad Halpha velocity profiles (FWHM less-than-or-equal-to 140 km s-1), and it is a radio continuum source. There is a rotating H I gas disk, 40 kpc in radius, at a position angle 51-degrees from the optical major axis. The central gas ridge follows the chain of H II regions, and the H I peak is on the hook. The outer gas on the southeast side curves away from the H I major axis. The central gas density is high, and the surface density declines very slowly with radius. The rotation velocity yields a mass of 1 x 10(11) M. at 3.3 Holmberg radii (R(H)). NGC 1800 has a hook that coincides with a large H II region, and an r1/4 luminosity distribution. There are numerous H II regions along the major axis and extraordinary filaments of ionized gas. Emanating from the major axis on either side of the galaxy are Halpha fingers 750 pc long. About 2.3 kpc to the north is a web of filaments approximately 3 kpc in extent. Halpha profiles of H II regions and filaments are narrow. The H i gas disk has a position angle that is approximately 13-degrees different from that of the optical axis. There are two peaks near the center, one of which is near the largest H II region. Beyond the Holmberg radius to the west is a 6 x 10(6) M. H I cloud. Its velocity indicates a mass of approximately 6 x 10(9) M. for NGC 1800 at 1.5 R(H). At approximately R25 to the east there is a large H I shell. Also, at approximately R25 on both sides the velocity gradient switches by 90-degrees, and in the interior the rotation is about the major axis. The central gas density is low and falls off slowly. In the inner regions NGC 4670 resembles an S0/a galaxy seen rather edge-on. It contains a central supergiant H II region with very high velocity widths (FWHM less-than-or-equal-to 180 km s-1) and complex velocity structures. It is a radio continuum source as well. The H I gas is a single spherical cloud or a disk at low inclination centered on the galaxy with a slight elongation along the optical major axis and rotation about the minor axis. The central gas density is high, and there is a high degree of concentration. The rotation speed indicates a total mass of 5 x 10(10) M. at 1.1 R(H). We compare these characteristics with properties of gas in the presence of stellar bar potentials, gas warps, and interacting and merging galaxy models. Although there are inconsistencies and uncertainties, we conclude that NGC 1140 is a spiral of low surface brightness that has undergone a merger, while NGC 1800 and NGC 4670 are, respectively, probably an Im system and a spiral that had an encounter of the Noguchi (1988a) kind.