We reanalyze microlensing events in the published list of anomalous events that were observed from the OGLE lensing survey conducted during 2004-2008 period. In order to check the existence of possible degenerate solutions and extract extra information, we conduct analyses based on combined data from other survey and follow-up observation and consider higher-order effects. Among the analyzed events, we present analyses of 8 events for which either new solutions are identified or additional information is obtained. We find that the previous binary-source interpretations of 5 events are better interpreted by binary-lens models. These events include OGLE-2006-BLG-238, OGLE-2007-BLG-159, OGLE-2007-BLG-491, OGLE-2008-BLG-143, and OGLE-2008-BLG-210. With additional data covering caustic crossings, we detect finite-source effects for 6 events including OGLE-2006-BLG-215, OGLE-2006-BLG-238, OGLE-2006-BLG-450, OGLE-2008-BLG-143, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. Among them, we are able to measure the Einstein radii of 3 events for which multi-band data are available. These events are OGLE-2006-BLG-238, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. For OGLE-2008-BLG-143, we detect higher-order effect induced by the changes of the observers position caused by the orbital motion of the Earth around the Sun. In addition, we present degenerate solutions resulting from the known close/wide or ecliptic degeneracy. Finally, we note that the masses of the binary companions of the lenses of OGLE-2006-BLG-450 and OGLE-2008-BLG-210 are in the brown-dwarf regime.