We present an analysis of the host galaxy dependences of Type Ia Supernovae (SNe Ia) from the full three year sample of the SDSS-II Supernova Survey. We re-discover, to high significance, the strong correlation between host galaxy type and the width of the observed SN light curve, i.e., fainter, quickly declining SNe Ia favor passive host galaxies, while brighter, slowly declining Ia's favor star-forming galaxies. We also find evidence (at between 2σ and 3σ) that SNe Ia are ≃0.1 ± 0.04 mag brighter in passive host galaxies than in star-forming hosts, after the SN Ia light curves have been standardized using the light-curve shape and color variations. This difference in brightness is present in both the SALT2 and MCLS2k2 light-curve fitting methodologies. We see evidence for differences in the SN Ia color relationship between passive and star-forming host galaxies, e.g., for the MLCS2k2 technique, we see that SNe Ia in passive hosts favor a dust law of RV = 1.0 ± 0.2, while SNe Ia in star-forming hosts require RV = 1.8+0.2−0.4. The significance of these trends depends on the range of SN colors considered. We demonstrate that these effects can be parameterized using the stellar mass of the host galaxy (with a confidence of >4σ) and including this extra parameter provides a better statistical fit to our data. Our results suggest that future cosmological analyses of SN Ia samples should include host galaxy information.