This is the second of two papers presenting a detailed long-slit spectroscopic study of the stellar populations in a sample of 36 ultraluminous infrared galaxies (ULIRGs). In the previous paper, we presented the sample, the data and the spectral synthesis modelling. In this paper, we carry out a more detailed analysis of the modelling results, with the aim of investigating the general properties of the stellar populations (i.e. age, reddening and percentage contribution) and the evolution of the host galaxies, comparing the results with other studies of ULIRGs and star-forming galaxies in the high-z Universe. The characteristic age of the young stellar populations (YSPs) is <=100 Myr in the nuclei of the overwhelming majority of galaxies, consistent with the characteristic time-scale of the major burst of star formation (SF) associated with the final stages of major galaxy mergers. However, the modelling results clearly reveal that the SF histories of ULIRGs are complex, with at least two epochs of SF activity. Overall, these results are consistent with models that predict an epoch of enhanced SF coinciding with the first peri-centre passage of the merging nuclei, along with a further, more intense, episode of SF occurring as the nuclei finally merge together. It is also found that, although YSPs make a major contribution to the optical emission in most of the extended and nuclear apertures examined, they tend to be younger and more reddened in the nuclear regions of the galaxies. This is in good agreement with the merger simulations, which predict that the bulk of the SF activity in the final stages of mergers will occur in the nuclear regions of the merging galaxies. In addition, our results show that ULIRGs have total stellar masses that are similar to, or smaller than, the break of the galaxy mass function (i.e. ULIRGs are sub-m* or ~ m* systems), and that the YSPs detected at optical wavelengths dominate the stellar mass contents of the galaxies. Finally, we find no significant differences between the ages of the YSP in ULIRGs with and without optically detected Seyfert nuclei, nor between those with warm and cool mid- to far-IR colours. While these results do not entirely rule out the idea that cool ULIRGs with HII/LINER spectra evolve into warm ULIRGs with Seyfert-like spectra, it is clear that the active galactic nucleus (AGN) activity in local Seyfert-like ULIRGs has not been triggered for a substantial period (>=100 Myr) after the major merger-induced starbursts in the nuclear regions.