Elder and eldest have only been used, in my knowledge, to refer directly to seniority within a family - my elder brother, my eldest sister. They are not used so much now as before (the words, not my brother and sister).
Even in that context, the use of eldest is limited.
I could talk about my eldest brother, Bill. But I couldn't say that Bill is the eldest boy in my family.
Yes, nowadays English-speaking people use older, oldest much more often. This, however, doesn’t mean that you won’t encounter elder, eldest as they appear in tests on English and there are some people who still use it. Old and its derivatives is applied to people as well as things.
I’d guess that if you refer to a group of senior people the elderly is used here and there’s no old-derivative counterpart—what would say our native friends?
According to the OED, for the most part, eldest and elder have been replaced by oldest and older.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.)