We present near-infrared spectroscopy and narrowband imaging at the wavelength of redshifted Halpha for a sample of 30 high-redshift, far-infrared luminous galaxies. This sample is selected from surveys in the submillimeter, millimeter, and radio wave bands and has complete redshift coverage with a median redshift of zsimilar to2.4. We use our data to measure the Halpha properties of these systems and to gauge the prevalence of active galactic nuclei (AGNs) in these galaxies through their [N II]/Halpha ratios and Halpha line widths. Removing obvious AGNs, we find that the predicted Halpha star formation rates in this diverse population are suppressed (by a factor of similar to10) compared to those derived from their far-infrared luminosities. Using the AGN indicators provided by our near-infrared spectra, we estimate that AGNs are present in at least 40% of the galaxies in our sample. To further investigate this, we construct a composite rest-frame spectrum for both the entire sample and those galaxies that individually show no signs of nuclear activity. We find [N II]/Halpha ratios for both composite spectra that suggest that the energy output of the galaxies is star formation rather than AGN dominated. However, we also find that the Halpha line in the composite non-AGN spectrum is best fitted with an underlying broad-line component with a narrow/broad flux ratio of 0.45+/-0.20. The median Halpha line width for our sample (removing obvious AGNs) is 400+/-70 km s(-1) (FWHM), and the typical spatial extent of the Halpha emission in our narrowband observations is less than or similar to4-8 kpc, which indicates a dynamical mass of (1-)x10(11) M-circle dot with corresponding dynamical times of 10-20 Myr. Using both high-resolution imaging and spectroscopically identified velocity offsets, we find that seven of the far-infrared luminous galaxies have companions, suggesting that they are undergoing interactions/mergers, and from their relative velocities we can determine a dynamical mass of (1.5+/-0.9)x10(11) M-circle dot. These measurements are comparable to millimeter CO estimates for the dynamical masses of these systems on similar scales and larger than recent estimates of the dynamical masses of UV-selected galaxies at similar redshifts derived in an identical manner. Using the [N II]/Halpha index to predict abundances, we investigate the luminosity-metallicity relation for these galaxies and find that many have metallicities consistent with UV-selected high-redshift galaxies and slightly lower than local luminous infrared and elliptical galaxies (although we caution that our metallicity estimates have possible systematic uncertainties). We also compared our Halpha and far-infrared luminosities with deep Chandra observations of a subset of our survey fields and use these data to further assess their AGN content. We conclude that these high-redshift, far-infrared luminous galaxies represent a population of massive, metal-rich, merging systems with high instantaneous star formation rates, strong dust obscuration, and actively fueled AGNs that are likely to be the progenitors of massive local elliptical galaxies.