If one has two elder brothers, is it OK to say "My eldest brother is this and the second eldest is that"?
Eldest is a superlative, while elder is a comparative. While you have two elder brothers, there can only be one eldest brother.
If you say,
My elder brother lives in Los Angeles, while my eldest brother lives in Chicago.
then the hearer would know that you have at least two elder brothers and that the oldest lives in Chicago.
I think that's fine, but other people evidently disagree. I found discussion of the topic of whether "second eldest" is a correct turn of expression in a court case, actually:
It is said, "second eldest" is not grammar; there can only be one "eldest". I do not agree in that. I suppose that it would be good grammar to say "A, B and C, are the three oldest men in the parish."
(Thellusson v. Rendlesham [1858-59], in The English Reports, Volume XI: House of Lords, Containing House of Lords Cases (Clark's), Volumes 7 to 11)