Else can mean ‘other’ or ‘more’ after words like somebody / someone / something / somewhere / anybody / anyone / anything / anywhere / everybody / everyone / everything / everywhere / nobody / no one / nothing /nowhere etc.

Do you need anything else? (= Do you need anything more?)
Why can’t you behave like everybody else?

Else can also mean ‘more’ after words like who, what, why, when, where, how, whatever, wherever etc.

What else did you get for Christmas?
What else have you got to do?
Whatever else he may be, he is not a writer.

Note that else comes immediately after the word it modifies.

What else do you want? (NOT What do you want else?)

Else has a possessive form: else’s

You are wearing somebody else’s coat.

Or else can mean ‘otherwise’ or ‘if not’.

Run, or else you will miss the bus. (If you don’t run you will miss the bus.)

Or else can also be used as a threat.
You had better stop hitting me, or else!

Elsewhere means ‘in, at or to some other place’.

If you are not satisfied with our services, go elsewhere.