[Grammar] She asked me who was my teacher.

[beachboy]

"Beachboy, who is your teacher?"

My friend asked me who was my teacher.
My friend asked me who my teacher was.

Are both sentences correct and have the same meaning?

 

[Tarheel]

I would only use the second one. But let's wait for additional comments. There might be other opinions.

 

[PaulMatthews]

"Beachboy, who is your teacher?"

[1] My friend asked me who was my teacher.
[2] My friend asked me who my teacher was.

Are both sentences correct and have the same meaning?

They have the same meaning, but only your second example is grammatically correct:

My friend asked me [who my teacher was].

The bracketed sequence is a subordinate interrogative clause (embedded question).

Subordinate interrogatives do not normally trigger subject-auxiliary inversion like that in [1], which is why the uninverted order in [2] is correct.

The meaning can be glossed as "My friend asked me the answer to the question 'Who was my teacher?"'

 

[GoesStation]

Are both sentences correct, and do they have the same meaning?

See above. The original sentence had a parallelism error: ​Are both sentences correct? [STRIKE]Are have the same meaning?[/STRIKE]