Reply To: Modeling wood pieces not oriented to the World XYZ
If your plank is Rotated in Object Mode, you can switch to Local Orientation.
Normal Orientation takes the Normal of your Edit Mode selection into account and with Vertices might give unexpected results:
For Vertex sliding I always use the shortcut G G. The Faces that need to stay flat, will stay flat with Vertex Slide. No matter what the orientation of your Object is. Just don’t try to move along an Axis. Moving along an Axis might work, but it depends on your Objects rotation and the Transform Orientation you’ve set.