Step 1: Recall the classification of aerial photographs by the tilt of the camera axis.
Aerial photographs are classified by the angle between the camera (optical) axis and the vertical (the plumb line, normal to the datum/ground plane) at the moment of exposure. A vertical photograph has the camera axis truly vertical, within a very small unavoidable tolerance. A tilted photograph has a small, unintentional inclination of the camera axis from the vertical, caused by aircraft motion. An oblique photograph has the camera axis intentionally and substantially inclined, tens of degrees from the vertical.
Step 2: Examine option (A).
Oblique photographs are obtained when the camera axis is not normal to the datum plane describes exactly the case where the axis deviates, by design, from being perpendicular to the ground, matching the definition of an oblique photograph. This statement is correct.
Step 3: Examine option (B).
Tilted photographs are obtained when the camera axis is tilted from the nadir line also correctly describes a tilted photograph; the nadir line is the vertical line from the camera through the ground point directly below, and an unintentional small tilt of the camera axis away from this line is precisely what defines a tilted photograph. This statement is correct.
Step 4: Examine option (C).
Vertical photographs are obtained when the camera axis is parallel to the datum plane is incorrect. For a vertical photograph the camera axis must be perpendicular (normal) to the datum plane, not parallel to it; an axis parallel to the ground would mean the camera is pointing sideways along the horizon.
Step 5: Examine option (D).
Vertical photographs are obtained when the photo plane is normal to the datum plane is also incorrect. The image (photo) plane inside a camera is always perpendicular to the camera axis. Since a vertical photograph has its camera axis perpendicular to the datum plane, the photo plane must be parallel to the datum plane, not normal to it.
Step 6: Conclude.
Statements (A) and (B) are correct, and (C) and (D) are incorrect.\[ \boxed{\text{(A) and (B)}} \]