nice thing about axles like this is if u do start taking it apart, it should be pretty easy to discover what's broken... and if you're not sure what the part is, you could always post a pic and I'm sure someone will know

 

Maybe the u joints on the driveshaft?

 

No, u-joints wouldn't cause the axle shafts to move in the housing. My brain keeps say spider gear... Not sure if that's right though. I've been up way too long to make accurate diagnostics haha!

 

If its the rear axle. Your tires are supposed to move about a half inch in and out. If it was 100% solid it would bind up tighter than a ticks ***.

 

U joints. I had a mercury 5.0 with all wheel drive. When i accelerated on the freeway it vibrated. And same with my dads camero.