Can the San Francisco Giants still make it to the playoffs?

There's an extremely small chance. They can't get a wildcard berth - Pittsburgh and Chicago have wrapped those up. They have to beat out the Dodgers who have a 5 game lead right now. The Giants would have to sweep the Dodgers in the next three games of the series. Even then, they need help from San Diego. San Diego would have to beat the Dodgers at least twice in the final three games while the Giants need to take 3 from Colorado (or 2 depending on the LA- SD outcomes).

The odds are against them, but never underestimate the choking Dodgers.

Yes, but it will very difficult. Giants can only make playoffs if they win the NL West.
Dodgers' magic number is 2. If Dodgers beat Giants in any of the 3 remaining games in SF this week, it's over for Giants.
Champagne was already on ice in the Dodgers clubhouse at AT&T Park last night

no

Next year

Possible. Not likely at all.

Go to http://mlb.mlb.com/mlb/standings/index.jsp. Look for the "E#" for the Giants. If there are Dodgers wins or Giants losses that total that number (it's currently 2) the Giants will be eliminated.

The Giants would have to win all of there remaining games, and the Dodgers can't win more than 1. Or the Dodgers would have to lose all of their games, and the Giants could lose no more than one.

Only IF the Giants win every game
and if the Dodgers lose every game left this season
otherwise they will be playing golf on Monday

Yup. Not mathematically eliminated yet.