On Diana, AP and CDR actually improve her effective tankiness because of her shield. However, an item with no resistances like Nashor's is only good as a late item or if you're very ahead. If you go Sorcs Nashor's Cap you'll do some decent damage right before you die almost instantly. If you get Zhonya's, Abyssal, Mercs, Cap and then late-game build a Nashor's, it will give you a lot toward your damage since you already have survivability with resistances + shield.
Nashor's isn't a bad buy on Elise, but I find it absurd to call it core. I'd rather get my CDR with a frozen heart, and I honestly don't care for the attack speed. Most time is spent in human form, and when I go into spider form, I usually swap back after my w time is up to get another human Q in.