If it squeaks, it's probably a case of dry,worn bearings. You'll have to disassemble the headset to get a proper look. You'll probably need to replace the ball bearings with new ones- the bearing cups are probably ok as long as they're not scored.

Bearing applications such as these require grease, not oil. I use white lithium grease on all bearings. Apply a generous amount to the bearing 'cup' and 'cone' surfaces when reassembling the headset. I spin the forks a few times before fully tightening everything up in order to spread the grease around the ball bearings.