Eileen and
Aileen both seem very dated.
Irene was never that widely used, so I don't tie it to a particular time; however, I do pronounce it with three syllables, which I greatly prefer to eye-REEN. I'd be less surprised to meet a little
Irene than a little
Eileen or
Aileen.
Confusingly, I knew a woman named
Aileen which everyone pronounced like
Eileen. The reason, if you can call it that, was that there was a family tradition of using A- names, and they'd run out!