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A spectroscopic survey of a sample of 200 luminous IRAS galaxies (LIGs: L_ir_^7^ > 3 x 10^10^ L_sun_; H_0_ = 75 km s^-1^ Mpc^-1^) was carried out using the Palomar 5 meter and University of Hawaii 2.2 m telescopes. Kim et al. (1995) described the data-taking and data-reduction procedures and presented line and continuum measurements extracted from the nucleus of these objects. In this paper, the nuclear data are combined with circumnuclear measurements on 23 of these galaxies to investigate the properties of the line-emitting gas and underlying stellar population in and out of the nucleus. The nuclear spectra of these galaxies were classified as H II region-like" or "AGN-like" using a large number of line-ratio diagnostics corrected for the underlying stellar absorption features. This correction is an important source of errors in some previous studies. The emission-line spectra of many AGNs were found to-be of relatively low ionization level and were therefore classified as LINER. We confirm that both the fraction of LIGs with AGN spectra and the fraction of Seyferts among the AGN increase with infrared luminosity, reaching values of 62% and 54% at the highest observed luminosities, respectively. The fraction of LINERs, on the other hand, is relatively constant at ~27%. The source of the ionization of the emission-line gas often is a function of the distance from the nucleus. Based on the emission-line ratios and the strengths of the stellar absorption features, circumnuclear starburst activity is a common feature of LIGs, regardless of their nuclear spectral types. The emission-line, absorption-line, continuum, radio, and IRAS properties of the LINERs suggest that most of the LINER emission in these infrared-selected galaxies is produced through shock ionization rather than photoionization by a genuine active nucleus. The nuclear region of Seyfert LIGs is found to be slightly less reddened than that of the LINERs and H II galaxies. The dust distribution generally is concentrated toward the nucleus, in agreement with the often peaky distribution of the molecular gas observed in these galaxies. Inverted dust profiles in which the nucleus appears less dusty than the circumnuclear region are observed in only three LIGs, all of which have AGN emission-line characteristics (one Seyfert 2 galaxy and two LINERs). Low nuclear dust content appears to favor the detection of active nuclei. This may be due to selection effects or may reflect real physical differences between these classes of objects: galaxies with Seyfert emission lines may be at a more advanced stage of dust destruction/expulsion than H II LIGs. Complex optical depth effects may also explain these results without invoking a smaller amount of dust in the nucleus. The Hβ and Mg I b absorption features are stronger in the nuclei of AGNs (especially among the LINERs) than in H II LIGs, suggesting that AGN LIGs are at a more advanced stage of stellar evolution than H II LIGs. Further support for this scenario comes from the fact that AGNs are found more frequently in advanced mergers than H II galaxies (only two Seyfert galaxies are detected in systems with well-separated nuclei). However, this last result may be a luminosity effect rather than an effect related to the dominant nuclear source of ionization. Moreover, the absorption-line data may simply reflect the fact that galaxies with powerful H II regions show evidence for young stars while galaxies with AGNs do not. The radial variations of the Hβ and Mg I b absorption features indicate the presence of a strong source of featureless continuum in the nucleus of nearly all LIGs, regardless of their nuclear spectral types. Contamination by the circumnuclear starburst prevents us from determining the extent of this continuum source. The [O III] profiles of both Seyfert and LINER LIGs were found to be broader on average than those of H II objects. Nearly 20% of the LIGs in our sample have line widths larger than 600 km s^-1^. We find that most of the galaxies in which we could determine the radial variations of the [O III] line width present broader profiles in the circumnuclear region than at the nucleus. When combined with published data on a few other well-studied LIGs, these results suggest that large-scale nuclear winds are common in these objects and are an efficient way of getting rid of the obscuring material in the nuclear region. The spatially extended LINER emission observed in many of these objects is probably due to shock ionization resulting from the interaction of the wind-accelerated gas with the ambient material of the host galaxy.