This may be obvious to many, but the way the open diff works is that the ring gear is turned by the pinion (super obvious). Attached to the ring is a cage that holds four small gears (the spider gears-sometimes also referred to as spider and sun gears). When the speed of the two wheels is the same, the ring turns the cage and the spider gears simply turn the output shafts but don't themselves rotate. When the speed of the wheels is different (for example when turning in a circle), the spider gears rotate so that the average speed of the two wheels matches the speed of the ring gear, but one turns faster and the other slower.
Below is a video of this.
If you are getting noise when the wheels are turning at different speeds, then either the spider gears themselves, or the bearings for the spider gears are shot.
I'd recommend you change the diff oil and try driving it gingerly for a bit. It may just be that the gears and bearings need to be exercised a bit. If the noise doesn't go away, then the spider gears and/or bearings have probably gotten rusty. You may be able to get it rebuilt, but I would caution against doing the yourself. You need a fairly large press, some special tools, and a set of spacer shims. It is really easy to mess up the setup, and if you do you will have put a lot of effort into a rebuild and end up with a junk differential with the ring and pinion gear faces worn through.
Below is a video of this.
If you are getting noise when the wheels are turning at different speeds, then either the spider gears themselves, or the bearings for the spider gears are shot.
I'd recommend you change the diff oil and try driving it gingerly for a bit. It may just be that the gears and bearings need to be exercised a bit. If the noise doesn't go away, then the spider gears and/or bearings have probably gotten rusty. You may be able to get it rebuilt, but I would caution against doing the yourself. You need a fairly large press, some special tools, and a set of spacer shims. It is really easy to mess up the setup, and if you do you will have put a lot of effort into a rebuild and end up with a junk differential with the ring and pinion gear faces worn through.