I have a 1995 Dodge Dakota. After a bit of freeway diving and everything is all warmed up the truck makes a rubbing/grinding/groaning noise, but only during sharp turns. Once I straighten the wheels back out the nose goes away. The noise doesn’t exist when it’s cold though.
Check the fluid level in the rear differential too. My truck is 4wd and sometimes gets a similar symptom – in my case it happens more on slow speed turns – but it is caused by the clutch discs in the rear limited slip differential not being lubed quite enough. Usually happens for me when the truck remains unused for several weeks, esp during a wet winter.
Four wheel drive Dakotas and Rams generally have limited-slip rear differentials, when the friction modifier (additive) degrades the clutches in the rear differential chatter. It is not broken, just unpleasant.
A rear differential service with the friction modifier added should cure the problem.
Carefully check the integrity of that boot. Is that sputz there on the right grease? And on that cable or line to the right further? If so, it appears it may be leaking grease. The boot is there to keep the grease on the inside. If that stuff does seem to be grease, suggest to clean off all that gunk on the boot as best you can and make sure the boot doesn’t have a split or tear in it. Don’t use any solvents to clean the boot though. That can damage an otherwise good boot. Check to make sure that circular clip that holds the small end of the boot tight against the shaft isn’t broke too.
First you got to figure out how the grease is getting out from inside the boot. If the boot is split, you have to replace it… That means either a new half shaft or some serious wrenching if you want to just replace the boot.
Since you have grinding noises during turns however, and you’ve already established grease is leaking out from that boot, I think what I’d do in this situation if it happened to my Corolla is to remove the outer CV joint from the shaft and inspect it on the bench. If there was any signs of the ball bearing or race damage, I’d replace the joint. If the surfaces looked ok but the grease was dry I’d clean everything up and install new grease and put it back together. On the Corolla anyway that’s a relatively easy job, since the entire shaft doesn’t need to be removed to just remove the outer CV joint. On some vehicles however this isn’t possible, or at least not very practical for a diy’er. For those vehicles it easier to remove the entire shaft, which is then usually just replaced with an aftermarket rebuild shaft.