As an investigation of the origin of "alpha-poor" halo stars, we analyze kinematic and abundance data for 73 intermediate-metallicity stars (-1 > [Fe/H] greater than or equal to -2) selected from Paper I of this series. We find evidence for a connection between the kinematics and the enhancement of certain element-to-iron ([X/Fe]) ratios in these stars. Statistically significant correlations were found between [X/Fe] and galactic rest-frame velocities (v(RF)) for Na, Mg, Al, Si, Ca, and Ni, with marginally significant correlations existing for Ti and Y as well. We also find that the [X/Fe] ratios for these elements all correlate with a similar level of significance with [Na/Fe]. Finally, we compare the abundances of these halo stars against those of stars in nearby dwarf spheroidal (dSph) galaxies. We find significant differences between the abundance ratios in the dSph stars and halo stars of similar metallicity. From this result, it is unlikely that the halo stars in the solar neighborhood, including even the "alpha-poor" stars, were once members of disrupted dSph galaxies similar to those studied to date.