I understand that zNear, zFar mark the clipping bounds of a scene. But OpenTK restricts the values to be greater than zero. Does this mean all my objects should be drawn on positive Z axis so that its not clipped ?
No, this is only the render clipping, after viewing translations. So if you render an object based at for example {0,0,-100} with your camera at {0,0,-110} it will still render if within the clipping planes, but stuff further then -110+zFar and -110-zNear will be clipped. That a pretty simple explanation, but in effect how it works.