One of my books and some of my friends say that torque and other angular quantities depend upon the perpendicular distance from the axis of rotation. This, in effect, would mean that translating your origin along the axis of rotation shouldn't change the torque or angular momentum of a body. Yet in another book, there is an example of exactly this phenomenon.
The other book and several other resources say that torque and other angular quantities depend upon the position of the object relative to the origin of the coordinate system.
To me, the perpendicular distance from the axis interpretation seems more natural.
Otherwise, imagine you have a door, free to rotate about only its hinges. If I place the origin of my coordinate system along the axis, I will measure some torque for a point on the door. Now, if I set my origin at some other location, according to the second interpretation, I would measure a different torque for the same point. This just seems wrong.