South Philly Chow/Karaoke?
I celebrated my birthday at Yakitori Boy. We reserved a private room for 3 hours and it was fantastic. Everyone had a great time and the food was reasonably priced and yummy. It's small plates, so we just ordered a bunch of different things. I had a large group and it was not a hassle to keep separate tabs.
I don't know of any Koren places on Washington Ave, except for a Korean BBQ place in the plaza at 6th Street (I think it's called International Smokeless BBQ), and I don't think they have Karaoke. Maybe you are thinking of the Korean places near Cheltenham Ave (North Philly)?
Maybe check out Yakatori Boy in Chinatown; they have private Karaoke rooms and, from what I have heard, pretty good food. 12 Steps Down (9th & Christian) has Karaoke some nights, and just got a good food writeup from Rich Nichols (menu created Mike Solomonov of Zahav fame), but that is not a sit down dinner type place.