relocating a 220V outlet
From the sound of it you have what you need to meet current requirements.
Get the proper size cable if you do intend to splice it, along with the proper splices (wire nuts, etc.).
If you are in doubt, cut a piece of the cable off and bring it to an electrical supply house (sorry, I don't trust home centers to get stuff like this right). They can provide you with a piece of cable, box and proper splices for the cables.
Upon re-hooking up the oven, splice the wires color for color and ground to green. Make sure you break the existing connection between the ground and white on the cable from the oven.
Sometimes I feel like if I answer any more questions it is like someone trying to climb over a fence to jump off a bridge and me giving them a boost.