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Eldest" may be used to emphasize rank or seniority while 'oldest' does not do this, and does not need to emphasize age. 'Eldest' is also used in comparing a group:
"my eldest son" or "the eldest of my three sons")
However, "oldest" can be used in a more absolute sense ("the oldest man alive").
'Older' and 'oldest' are used of people or things, but 'elder' and 'eldest' are used only of people, and only for members of the same family.
"Dave is older than my cousin."
"John is the oldest man in the organization."
"Sam is Sally's elder brother."
"I have three sons; Paul is the eldest."
There is no real semantic difference between the two, but by common convention, "eldest" is used strictly with respect to people, while "oldest" can be used in reference to any object including people.
'Elder' cannot be used in comparisons: "Jane is older than Mary." (not 'elder than')
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