New optical and infrared observations along the sight-line toward the quasar OI 363 (0738+313) are presented and discussed. Excluding systems which lack confirming UV spectroscopic observations of the actual Lyman alpha line, this sight-line presently contains the two lowest-redshift classical damped Lyman alpha (DLA) quasar absorption line systems known (i.e. with N(HI) ge 2 x 10^{20} atoms cm^{-2}), one at z(abs)=0.0912 and the other at z(abs)=0.2212. The z=0.09 DLA galaxy appears to be an extended low surface brightness galaxy which is easily visible only in infrared images and shows rich morphological structure. Subtraction of the quasar nuclear and host light yields L_K approx 0.08L_K* at z=0.09. The impact parameter between the galaxy and quasar sight-line is very small, b<3.6 kpc (<2 arcsec), which makes measurements difficult. The z=0.22 DLA galaxy is an early-type dwarf with a K-band luminosity of L_K approx 0.1L_K* at impact parameter b=20 kpc. In general, these results serve to support mounting evidence that DLA galaxies are drawn from a wide variety of gas-rich galaxy types. (Abridged)