I'd like to first say, "Welcome to the forums!" We're a friendly bunch and value your participation...
Yes, you have a Dana 300 transfer case, and once clean and free of all that debris, rebuilding this unit can be a very fruitful project. I cover the step-by-step rebuild of the Dana 300 in my Jeep CJ Rebuilder's Manual: 1972-86 edition (Bentley Publishers). Many have found the book valuable for restorative work on these year models. Importantly in your case, I personally took a CJ-7 to the bare frame, with the tub and fenders still mounted, and rebuilt each powertrain, gear and axle component. The Jeep had the AMC Model 20 rear axle and a 2.5L four banger that I replaced with a 4.2L inline six and Mopar retrofit EFI. There were other upgrades that I included, too.
If you have either a factory shop manual or my book, I can fill in the repair or restoration blanks for any and everything related to your Jeep. Other members have an intimate sense for these models as well...I've rebuilt the front and rear axles, can address the steering gear (manual or power) and linkage, the engine, the cooling, the brakes, wiring, whatever! Happy to provide details that you might need.
Additionally, if you do post photos and follow the steps in either my book or an AMC/Jeep factory manual, others will benefit greatly. In my view, this is not the kind of transfer case, or vehicle as a whole, that can be "restored" without a guidebook. My step-by-step procedures in the CJ Rebuilder's Manual are far better illustrated than the factory manual. However, I have a wall full of factory workshop manuals that have served me well, both as a professional mechanic and author. Having instructed automotive technology and welding, writing curriculum in the process at the adult education level, I would safely describe my books as helping readers "think like a mechanic". That's always been my goal, from the first edition of the Jeep Owner's Bible forward.
Advance Adapters, one of the magazine's valued sponsors, sells my books, as do other sources in the aftermarket. (Of course, Bentley Publishers offers the books.) The AMC/Jeep factory workshop manuals turn up at eBay, and I found the 'reprint' of the 1984-86 AMC/Jeep factory manual at Amazon: http://www.amazon.co...f=pd_cp_b_sexpl.
I actually have an original of this M.R. 252 AMC/Jeep manual in my library. It has been a great resource over many years of work on 1980-86 Jeep CJ-5s (up to '83), Jeep CJ-7s and the Jeep CJ-8 Scrambler. From my experience, shop manuals are essential for the kind of work you anticipate doing here. The cost of these books will pay for themselves many times over as you perform the work "by the book" and wind up with a reliable and safe, "as new" Dana 300 transfer case, Dana 30 front axle, AMC Model 20 or Dana 44 rear axle, Saginaw steering gear or whatever you tackle.
Trust this is helpful, Forman...Happy to assist whether you decide to "wing it" or follow prescribed shop manual guidelines...Other forum members will join this discussion, I'm sure...