Is there any way to explain this?
It would be easier to see with the blend file here... but looks like all the bones in the Character are aligned to the normals.
Look in the Outliner if you can separte it from the geometry and try to build a armature scheme native from blender.
The rig for this model was not really designed to look good in Blender—it was probably created in Maya or something. This is what's creating the strange appearance. You have a few options:
1) Delete the rig and create your own from scratch. Just hit X to delete the rig.
2) Manually fix every single bone to look good. (This will take extensive time and effort for potentially little reward.)
3) Deal with it. Just play around with it a little until you figure out the rhyme and reason behind the rig. Get used to it, and then use it all you like.