Older vs Elder

Elder and eldest can be used instead of older and oldest to talk about the order of birth of the members of a family.

They are only used attributively (before nouns).
Compare:

• My elder/older brother has just got married.

He's three years older than me. (NOT ... elder than me.)

• His eldest/oldest daughter is a medical student.

She's the oldest student in her year.

Elder brother/sister are used when a person has only one brother/sister who is older; eldest is used when there are more.

• elder son/daughter is the older of two; 
• eldest son/daughter is the oldest of two or more.