We present a second paper of a complete characterization of stars whose low-depth transits were discovered by the OGLE-III campaign to select the most promising candidates for spectroscopic confirmation. This paper follows a similar analysis to one previously performed in Gallardo et al. (2005, A&A, 431, 707). We present new optical and near-IR photometry and derive physical parameters such as effective temperature (Teff), distance (d), the stellar radii (R_ast), and the companion radii (Rc). We selected eight M (2800 K ≤ Teff ≤ 3850 K) or K (3850 K ≤ Teff ≤ 5150 K) stellar objects as potential candidates to host exoplanets, even though, considering the radii of their companions, only the stars OGLE-TR-61, OGLE-TR-74, OGLE-TR-123, and OGLE-TR-173 are the most promising M-type transit candidates to host planets. A confirmation of the planetary nature of any of these objects would be extremely valuable in providing a means of characterizing planets transiting M-type dwarfs with effective temperatures down to only 2900 K.