We present near-infrared spectroscopy and narrow-band imaging at the wavelength of redshifted Hα for a sample of 30 high-redshift, far-infrared luminous galaxies. This sample is selected from surveys in the submillimeter, millimeter and radio wavebands and has complete redshift coverage with a median redshift of z ∼ 2.4. We use our data to measure the Hα properties of these systems and to gauge the prevalence of active galactic nuclei (AGN) in these galaxies through their [NII]/Hα ratios and Hα line widths. Removing obvious AGN, we find that the predicted Hα star formation rates in this diverse population are suppressed (by a factor of ∼ 10) compared to those derived from their far-infrared luminosities. Using the AGN indicators provided by our nearinfrared spectra, we estimate that AGN 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 for those galaxies which individually show no signs of nuclear activity. We find [NII]/Hα ratios for both composite spectra which suggest that the energy output of the galaxies is star-formation-rather than AGN-dominated. However, we also find that the Hα line in the composite non-AGN spectrum is best fit with an underlying broad-line component with a narrow/broad flux ratio of 0.45 ± 0.20. The median Hα line width for our sample (removing obvious AGN) is 400 ± 70 km s −1 (FWHM), and the typical spatial extent of the Hα emission in our narrow-band observations is < ∼ 4-8 kpc, which indicates a dynamical mass of 1-2×10 11 M ⊙ 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 × 10 11 M ⊙ . 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 [NII]/Hα 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 Hα 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 AGN which are likely to be the progenitors of massive local elliptical galaxies.