Elderandeldestmean the same asolderandoldest. We only use the adjectiveselderandeldestbefore a noun (as attributive adjectives), and usually when talking about relationships within a family:
Let me introduce Siga. She’s myeldersister.
Not: …She’s my sister. She’s elder.
It’s Catherine’s eightieth birthday on Thursday and she is now theeldestmember of the family.
We also useelderandeldestas nouns:
Jack is theeldestof four brothers.
Olderandoldestare used in similar ways:
Myoldersister is coming to stay with us at the weekend.
Matt is theoldestof our children and Simon is the youngest.
Olderandoldestcan be used to refer to the age of things more generally:
The town hall is by far theoldestbuilding in the whole region.
Not:The town hall is by far the eldest building…
We can useolderandoldestafter a linking verb (as predicative adjectives):
I think her grandfather must beolderthan her grandmother.
Not:I think her grandfather must be elder than…