I have bought a use XC 70 2003 and I don't think it's work properly. I'll try to explain how it react in diverse situation.

When the car is on 4 jackstands, and i accelerate, the rear wheels engage, what is normal if AWD work properly. BUT, on a steep dirty road, and even on a wet pave, my front wheel spin a lot and rear one doesn't;

The rear end on the air, if I tourn one wheel, by hand, the other one don't move. I've changed oil of rear differential for the proper one with antislip aditive and the old one was pitch black, it change nothing;

When i drive it I can hear sometime some big jerk that I can feel in the body. Specialy when i tourn on left and give some gas. I have the feeling it cme from the rear. This is new it didn't do that when I bought the car.

On the field, if the front wheel left and the rear right is loaded, and the other two is free, there is no traction and I can't move.

Is someone have any idea of what could be the problem ?

 

It sounds like you have a problem with your visco coupler. This coupler allows the driveline to slip when you make turns because the outer wheels turn faster than the inner. When it stops working the drivetrain binds on turning and pops when the pressure reaches a threshold and slips. Disconnect the driveline at the rear and drive the car to see if it still binds on turns. If not I suspect you need a new coupler. Hope this helps