the waitstaff are in tuxedo jackets, if that helps any. its a tablecloth place, and while not super formal, dressing in a jacket or nice shirt is common & best.
i would not recommend jeans & casual shirts/tees... probably could, mind you, but it just sorta cheapens the atmosphere for fellow diners.
Depends what the jeans and shirt are like. If the shirt is a crisp shirt with a collar, you'll be fine, and the jeans with the elastic waistband and the loop for the hammer probably won't do. And I'd say sneakers are out. I don't think Irene's has a formal dress code, but I'd aim for dressy casual.