What is the most succinct way of explaining that I have an older sister and a younger sister?
我有一个姐姐和一个妹妹


This is good.


  我是三个姐妹中中间的一个


This is usually expressed in another way: "我家一共姐仨，我是老二", or "我妈(我爸)有三个闺女，我是老二".


  我有两个姐妹


It might work, but I don't often hear it.

And by the way, maybe related to his question or not: If one says "我有两个兄弟"， it often means he has two younger brothers (and gives no information about how many older brothers he has), but not two brothers (in all). As fas as I know "姐妹" does not have such usage.