Here is a list of Los Angeles Dodgers who have hit 3 home runs in a game, in order of my estimation of most likely to least likely to have accomplished the feat:
Shawn Green 2001, 2002
Green did it twice. When his swing was right it was gorgeous, and so were the results. When his swing was wrong he kept opposing second basemen very busy. The 2002 occurrence was actually a four HR game, in which he set the major league record with 19 total bases in a nine inning game.
Mike Piazza 1996
Piazza was certainly a better player than Green, but in his prime Green hit more home runs than Piazza, and I figure the guy who did this twice really should be most likely.
Jimmy Wynn 1974
Wynn was very good hitter, though not an especially prodigious home run hitter. He did have 32 HR in 1974.
Andre Ethier 2009
Tonight's hero. Someday it might seem more likely that Ethier did it than Wynn, but for now I have Wynn ahead a little bit.
Hee Sop Choi 2005
Choi is one of three LA Dodgers to have a three home run game in his last major league season. Which is really strange. Choi was known as a home run hitter, but he didn't really hit that many. He was more well known, at least by me, for being behind Jason Philips on the first base depth chart for awhile in late 2005. Jim Tracy didn't really like him. He would have had about 30 home runs in 2005 if he had played every day. Instead he had 15, including 6 against the Twins in one memorable interleague series. Perhaps Ethier can match him.
Davey Lopes 1974
Joined Wynn in the triple homer game club in 1974, but he wasn't nearly the home run hitter Wynn was, having only 10 on the season. He did hit 28 in a season later in his career.
Kevin Elster 2000
It's a miracle Elster isn't last on this list. Not only was 2000 his last major league season, but he didn't even play in 1999. And yet Elster was actually a pretty good hitter in 2000, hitting 14 home runs and posting his only season with an OPS+ above 100, not counting an early season when he played in only 5 games. If this list was ranked on glory of the feat rather than on likelihood of the feat Elster would easily come out ahead, since his three home run game came in the first game ever played at Pac Bell Park. The Giants must have been so surprised to see Kevin bleeping Elster ruining their inauguration of the new digs.
Cory Snyder 1994
It took Cory Snyder to beat out Kevin Elster for most unlikely three homer game. Snyder had only 6 home runs in 1994, and three of them came in a crazy early season 19-2 thrashing of the Pirates. He was pretty lousy the rest of the year and by the middle of August he had seen the last of the big leagues forever. Cory is not the only Dodger Sn(y|i)der to hit three home runs in a game, by the way. His more famous homosurnym-mate Duke Snider hit three homers in a game twice but both came in Brooklyn.
Unfair Win Shares ( Dodgers )
Ethier -- 2
Kershaw -- 1
Unfair Loss Shares ( Mariners )
Beltre -- 1
Johjima -- 1
Vargas -- 1