We present a study of the nearby post-merger giant elliptical galaxy, NGC 5128 (Centaurus A), in which we use the properties of its globular cluster (GC) and planetary nebula (PN) systems to constrain its evolution. Using photometric and spectroscopic data for 215 GCs presented in Paper I, we study trends in age, metallicity, and kinematics for the GC system. We confirm that the GC metallicity distribution is bimodal, and show that these two sub-populations have different properties. Using spectral line index measurements of the brightest clusters, the metal-poor GCs have old ages like the Milky Way globular clusters, while the metal-rich GCs have H-beta line-strengths that could be interpreted as a mean age of ~5 (+3/-2) Gyr. Both populations appear to have [Mg/Fe] ratios consistent with that of the Galactic GC system, although this quantity is not very well-constrained. The kinematics of the metal-rich GCs are similar to those of the planetary nebulae, exhibiting significant rotation about a misaligned axis, while the metal-poor GCs have a higher velocity dispersion and show a weaker kinematic correlation with the field stars. The total gravitating mass of NGC 5128 derived from the GCs is in excellent agreement with the value derived from stellar (PN) kinematics. We suggest that these and other data support a picture in which the main body of NGC 5128 was formed 3-8 Gyr ago by the dissipational merger of two unequal-mass disk galaxies supplemented by the continual accretion of both gas-rich and gas-poor satellites.