Elder vs Older/Elder vs Eldest

There are four items: Older, Oldest, Elder and Eldest.

The difference between Older and Oldest, and between Elder and Eldest is obviously that the ones that end in -er are comparatives whereas the forms that end in -est are superlatives. The difference between Older and Elder, and between Oldest and Eldest is not so obvious, but Use of English says that the ones starting with an E- are limited to talking about people and, most commonly, about family members. In contrast, the forms starting with an O- are most generally used:

My elder/older sister lives in that building over there. The building is the oldest/eldest in the area.

Also, the E- forms are used as an adjective before the noun whereas the O- forms are not restricted to a prenominal position. This is a very important difference.

My sister is older/elder than me.

Elder can also be used as a noun; it's a historical term to describe the wise old people of a tribe or settlement:
The village elders discussed the problem.

The other choice is that of deciding whether to say my elder sister or my older sister. In theory, that depends on the number of sisters you have and who you are referring to. If you have just the one sister, you'd refer to her as your elder sister. BUT if you have, let's say, two sisters who are older than you, and you talk about your eldest sister, that would be the one that was born first, your elder sister being the one born between her and yourself. 

I've got two sisters who are older than me. My sister Ana is my eldest sister. My sister Cristina is my elder sister. Ana was born, then Cristina, then me.

You see? That's in theory. In practice, they're pretty much interchangeable when talking about family.
And in any case, most native speakers would talk about "my big sister" (meaning older than me) or "my little brother" (meaning younger than me).