My obliques are sore, I think from PR deadlifts that I did yesterday, because all I did other than that was squats (not PR... rebuilding from a deload), and bench press. I've felt this before, too.
What part of the deadlift works the obliques?
The obliques mildly assist in flexion of the torso, and part of their attachments include the sheath of the rectus abdominus (abdominal muscle) and the linea alba (tendonous side attachment that serves as a connection and brace for the external oblique and abdominus).
The primary thing that they are going to be doing during your deadlift is stabilizing the torso, and when you are doing things like maximal/PR type lifts, you engage muscles more than you might normally.
So, you activate them for stabilization, and keep them tense throughout, which will give you elements of isotonic, eccentric and concentric contractions throughout the exercise. They are all a system combined with the abdominals. They also assist in breathing and a few other functions unrelated to torso rotation.