The damage reduction from Drunken Rage is applied when you start drinking, try to use it when you see damage coming your way.
Try to knock enemies back into your towers with Explosive Cask.
Try to combo Body Slam with Explosive Cask to set up kills for your team.
Gragas can knock everybody away with his ultimate. Be careful that you don't get knocked into him or, worse, an enemy tower.
Body Slam is on a very low cooldown, making it difficult to pursue Gragas. Don't overextend yourself chasing him.