This is a quick trick I used to fix some of my cords that had become hopelessly twisted. It's not a guaranteed fix - but it does a great job at improving the condition. Think of it as laser-tatoo removal without all the pain.
Step 1: It's OK. Help Is on the Way - Here's All We Need
The drill can be corded (gasp) or battery powered.
You can actually use almost any tape you want.
Step 2: Quick Assembly
Step 3: Insert Bolt Into Drill
Step 4: Tie the Other End of Cord to a Tree or Post
Step 5: Regain Control of Unruly Extension Cord
Also - Very Important! Before "unwinding", stretch the cord so it suspends off of the ground by a few feet. This will help a great deal because it will allow the "bad twist" to be worked on somewhat evenly across the length of the entire cord.
So, now just unwind with the drill! I have found that doing a little "extra" twisting helps to straighten things out more. It's no exact science, but it works for me!
OK - once your'e happy with the cord, be sure to wind and store properly. And keep away from those who are the "bad-winders".
Step 6: Notes on How One Might Properly Coil the Cord
I'm going to let the pictures tell the story...