Agree with the above, and if I may add some info, hope it isn't too boring...
If you were to drive your car in a constant circle (such as skidpad etc.) and trace the path followed by the inside wheels vs the outside wheels- the two circles would be different size (by approximately the track width of the car). When turning, the outside wheels spin at a faster rate than the inside wheels. Something has to allow for that to happen without binding in the drivetrain- that's where the differential comes in. One of the characteristics of a basic differential is that it gives torque to the wheel that can turn easiest. Many people don't realize it, but theoretically it is possible to get such a car stuck by having just one of the drive wheels on a patch of ice (etc.). So, a "2wd" car with basic differential is really only 1wd, and a 4wd truck with basic differentials is really only 2wd. In the "old" days, if you took out mom or dad's car and stomped on the accelerator to spin the wheels away from a stoplight, you'd often find there was just one black stripe on the ground- for that same reason. Some cars and trucks were (are) available with something called a limited slip differential. There are different approaches to implementing this, but the bottom line is the limited slip unit partially binds the two wheels together, so all the torque cannot go to one side. One of the areas where this is highly beneficial is in rapid acceleration, where more power can be applied before wheelspin occurs (because both wheels are being driven, not just one). Limited slip also offers benefits in mud, off road etc. I believe the GM (Chevy etc.) designation for their limited slip option was (in the 60's, 70's etc.) "positraction", and that moniker has become often applied in general (like saying you want a kleenex, when kleenex is really a brand name). This is where you hear people ask "does it have posi ?". (cars with this equipment will make two black lines on the road, assuming the engine has enough power....) Even for our VWs there are aftermarket limited slip differentials available. Not sure what's current because I don't dabble much in the hot rod side of vws, but there was at one time a company named Quaife (sp?). If someone listed Quaife among their mods, that generally meant the car had a limited slip differential. Drawback to limited slip is that it can increase binding in tight maneuvering.
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Back to OP original question- I agree with Alchemist- looks like a CV joint or something in the axle shaft has broken on one side. I'd recommend no more effort to move it with the engine, lest something tear loose and the flailing axle shaft bashes something up. Have the car towed home (or to trusted shop etc.) and replace the axle shaft.
