As of Blender 2.79 you can reproject strokes to existing surface or just to make them planar.
When drawn over some objects from some projection (top one in your case) they look as expected from that projection:
If moving viewport projection problems will become apparent:
To fix that first hide or delete any other objects except for the one you're going to use as a new level for projection. Also make sure that mesh for the projection (probably plane) is larger when seen from the top view than all the strokes.
Then enter Edit Strokes mode, A to select all. Open Toolshelf, choose Grease Pencil tab. Open Edit Strokes rollout and on its bottom find Reproject Strokes dropdown. Choose Surface there to use surface of the mesh you want instead of planar projection depending on the current viewport camera position. Your drawing will be brought to the surface of the mesh you used as a new level.