I'm assuming you're on stock axles. Being an 85, I'm assuming they're wide track, but stock gearing (2.72?). To run 38's, you'd at the very least need a re-gear. Then would come the 1-piece shafts, upgraded axle shafts in the front, etc. etc....Are you trying to stay street legal? I don't have any idea on DOT regulations in Oregon, but an axle swap wouldn't be out of the question. At any rate, people have run 38" tires on stock CJ axles, but you'd be running them on borrowed time offroad, unless you're VERY careful on some very mild trails.
Anyway, to fit that much tire, you'd have to run a spring over conversion. It is possible to get the correct aftermarket components to correct your steering angles in the front, but I'd recommend a Chevy 44 front (or a 60, if you've got some spare coin laying around) for this...much easier, as they typically come with flat-top knuckles so you can run crossover steering.
Along with the SOA, you'd still have to do some fender trimming to get full flex. The good thing with SOA is you have increased wheel travel over the stock configuration...BUT -- if you run stock springs, they will tend to wear out much quicker since they can go so much more into negative arch.
Going SOA will also need some sort of traction control in the rear, i.e. a ladder bar or something of the like. There are many write-ups on the interweb with good (and bad) examples of making one while still retaining full axle articulation.
As far as rear driveshaft angles, you'd need to likely go with a CV joint to keep the driveshaft from being quite so steep...this will let you point the rear differential up toward the
Transfer Case , helping flatten out your upper joint angles.
FWIW, I've got 38.5 Boggers under my CJ with a SOA setup. I've got stock CJ leaves in the rear with Chevy 1/2 ton springs in the front. I can tell you that the rear tires do rub the front of the rear fenders at full flex...I'm contemplating moving the rear back a few inches to get rid of the rub. If you do something like this, you'll have to use a fuel cell, because the differential will try to occupy the same space as your fuel tank. Moving the front axle forward a few inches will also help. On that note, you'd need new driveshafts.
Long story short, putting that much tire under a CJ requires a lot of thought, research, time, and patience. Not impossible by any means, but definitely can be a daunting task.