It's really annoying when somebody "helps" you clean up by improperly coiling your power cords. The main way this happens is illustrated in the first picture. The person grabs the end of cord in one hand and then tightly wraps the cord around his or her elbow and hand repeatedly. This guilty twister is usually an impatient Type-A that thinks fast and hard is better. Here's a public service announcment: Fast and Hard is Not Better.
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
This one is easy. All I used is a drill, an eyebolt, and some masking tape.
The drill can be corded (gasp) or battery powered.
You can actually use almost any tape you want.
Step 2: Quick Assembly
Now, just attach the cord to the eyebolt. It can be done a number of ways. I have illustrated two ways.
Step 3: Insert Bolt into Drill
Now mount the bolt into the drill.
Step 4: Tie the other end of Cord to a Tree or Post
Now just stretch the cord out all the way and tie the other end of the cord to a fixed tall stable object. A tree or swingset post are good candidates.