We have used the VLA B and C Arrays to make 21 cm H I observations of the peculiar galaxy NGC 2782 (Arp 215). These observations are complementary to previously published D Array VLA data, which revealed the presence of a long (5' ~ 54 kpc) H I plume near the western side of this galaxy. We have also obtained BVRI Hα images of the main body of this galaxy using the McDonald Observatory 30" telescope. The optical images of this galaxy show a strong stellar tail extending to the east, opposite the H I plume. Within the disk of NGC 2782, unsharp masking of the optical images at all 4 broadband wavelengths reveals three bright "ripples", separated by ~15". The light profiles across these ripples are symmetrtc, without a sharp outer edge. Hα is strong at the starburst nucleus and along the northern and western sections of the inner ripple. The ripples are not significantly bluer than the interripple disk, except in regions with strong current star formation as seen in Hα. The eastern stellar tail is somewhat bluer than the interripple disk in the parent galaxy, with colors typical of tidal tails. No Hα is seen from this eastern tail. Optical images are not available as yet of the western tail. The new higher resolution H I data show that the atomic gas is very clumpy. We have identified ten H I clumps in the long Western plume, with H I masses of ~10^8^ M_sun_, similar to those of dwarf galaxies, and column densities of ~10^21^ cm^-2^ over surface areas of ~10 kpc^2^. No CO (1-0) emission has been detected from this plume, suggesting that it is material stripped from the outer edge of a disk galaxy. The H I is enhanced along most of the inner ripple, and clumps in the HI are generally associated with clumps in the I band. The Hα peaks, in contrast, are generally not coincident with H I peaks. No H I is seen at the tip of the eastern extension. The H I distribution near this structure is ring-like rather than tail-like as in the optical data. We have detected redshifted H I absorption toward the central continuum source, indicating gas infall into the nuclear region. The H I velocity field for the inner region shows the typical signature of an inclined, rotating disk. This disk appears to be counterrotating with respect to the motions of the large scale tidal structures. Using a restricted 3- body dynamical model, we have successfully reproduced the basic properties of NGC 2782 with an off-center collision between two galaxies, where a lower mass disk companion (M_2_/M_1_~0.25) collides almost head- on with a larger disk galaxy. In this scenario, the companion becomes the eastern extension, and the long western tail is material pulled out from the larger galaxy. The lack of H I at the tip of the eastern tail may be due to stripping during the collision. Alternative formation scenarios include a merger or interaction between two disk galaxies, where the ripples may be due to a disturbed spiral density wave or galactic winds due to the central starburst.