We have mapped the kinematic and physical properties of gas emitting optical emission lines across 39 gas-rich mergers, some of which we have shown to host tidally-induced gas inflows, with deep ESI spectroscopy. In our unique analysis of these longslit spectra, we fitted multiple kinematic components to forbidden lines and recombination lines simultaneously, enabling an examination of the excitation mechanism in different kinematic components. We identify many rotating gas disks in systems whose stellar component is no longer a disk due to the merger. Many of these disks present gas excited by hot stars, but some of the disks present shock-like ratios of diagnostic emission lines, an observation we attribute to the collision of the two galaxies. In another subset of galaxies, we find very broad (sigma > 150 km/s) emission components that also present shock-like emission-line ratios. The large spatial extent of this emission favors shocks over the narrow-line region of a hidden AGN as the excitation mechanism. The high star formation rate, high dust content, and blueshift of the broad emission further suggest an origin in a galactic outflow. If this interpretation is correct, then our study of these nearby galaxies provides important insight for interpreting the broad emission lines associated with giant star-forming clumps in z~2 galaxies. It also shows that galactic outflows can be recognized via resolved emission lines, in addition to absorption lines, even in integrated spectra; and this technique could prove very powerful for studying galactic outflows in infrared spectra of high-redshift galaxies in the future.