I have a 220 V line in my kitchen for an oven. We are remodeling the kitchen and moving the oven and, thus, need to move the 220 V outlet.
- Can I extend the line by joining cables in a junction box and moving the outlet where it needs to be?
- Can I just have a long cord (6–10 feet) from the oven to the original location of the outlet?
Here is a photo of what my outlet currently looks like 
Here is the inside: 
It may be hard to see, but there are only three wires, no ground.
Here is another picture of the inside of the box. You can’t see very well outside of the box. There is a ground wire attached to the metal box. There is no conduit. There should be something (I don’t know what it’s called) that clamps the wires as they come into the box, but there isn’t.
Best Answer
You'll have to pull the box out and rearrange things
While it sounds like you have all the correct wires available to extend this on as a four-wire connection to your new range location, your last installer forgot the clamp for connecting the cable to the box, and also made the ground connection outside the box, which isn't right either. So, you'll have to carefully remove the box, get a suitable box (I'd recommend a big box such as a 4-11/16" or even a 5" square for this since it's going to get blanked anwyay), get a cable clamp that can handle a 6/3 with ground SER (not just NM) cable in a 3/4" KO, and refit the box with the cable properly locked in the clamp (the cable jacket needs to extend 1/4" past the inside of the cable clamp) and the box grounded on the inside using a 10AWG solid pigtail to a 10-32 grounding screw in the tapped hole on the back of the box, then nutted to the existing grounding wire.
From there, since you have all four wires, you can extend it to the new location with the largest wirenuts you can get (rated for 2×6AWG), a length of 6/3 W/G NM cable, and a 3/4" NM clamp (you can use the plastic button-style for this side). Of course, you'll need a box (and another 3/4" NM clamp, if your box has knockouts in it) at the new location as well, as well as a similar grounding arrangement as the replacement box if you're using a metal box for the new box. Note that you'll need to fit a proper NEMA 14-50R (instead of the existing NEMA 10-50R) for the new receptacle and change the oven over to a four-prong range cord from the three-prong cord it was using as part of this work, too.