In Papers I and II of this series, we have found clear indications of the existence of two distinct populations of stars in the solar neighborhood belonging to the metal-rich end of the halo metallicity distribution function. Based on high-resolution, high S/N spectra, it is possible to distinguish between ``high-alpha'' and ``low-alpha'' components using the [α/Fe] versus [Fe/H] diagram. Precise relative ages and orbital parameters are determined for 67 halo and 16 thick-disk stars having metallicities in the range -1.4<[Fe/H]←0.4 to better understand the context of the two halo populations in the formation and evolution of the Galaxy. Ages are derived by comparing the positions of stars in the logT
eff-logg diagram with isochrones from the Y
2 models interpolated to the exact [Fe/H] and [α/Fe] values of each star. The stellar parameters have been adopted from the preceding spectroscopic analyses, but possible systematic errors in T
eff and logg are considered and corrected. With space velocities from Paper I as initial conditions, orbital integrations have been carried out using a detailed, observationally constrained Milky Way model including a bar and spiral arms. The ``high-alpha'' halo stars have ages 2-3Gyr larger than the ``low-alpha'' ones, with some probability that the thick-disk stars have ages intermediate between these two halo components. The orbital parameters show very distinct differences between the ``high-alpha'' and ``low-alpha'' halo stars. The ``low-alpha'' ones have r
max's to 30-40kpc, z
max's to ∼18kpc, and e
max's clumped at values greater than 0.85, while the ``high-alpha'' ones, r
max's to about 16kpc, z
max's to 6-8kpc, and e
max values more or less uniformly distributed over 0.4-1.0. A dual in situ-plus-accretion formation scenario best explains the existence and characteristics of these two metal-rich halo populations, but one remaining defect is that this model is not consistent regarding the r
max's obtained for the in situ ``high-alpha'' component; the predicted values are too small. It appears that
{omega} Cen may have contributed in a significant way to the existence of the ``low-alpha'' component; recent models, including dynamical friction and tidal stripping, have produced results consistent with the present mass and orbital characteristics of
{omega} Cen, while at the same time including extremes in the orbital parameters as great as those of the ``low-alpha'' component.
