According to the OED, for the most part, eldest and elder have been replaced by oldest and older. There are some cases where they are still used: when refering to family members as pjd mentioned, in the military and government (elder senator or eldest batallion), and in card playing (the eldest hand).
Personally, I would always use oldest, except in the case of a senator, where the elder senator refers not directly to his age, but rather his years in office. (In the US each state has two senators, and the one serving the longer is usually also the older. Even in this case it seems as though elder is being replaced by senior.)