Not sure how this occurred or what mod caused it, but Khajits in my game now have texture problems with their hands, upper torsos, and tails. What DDS files do I need to refresh or replace, and from where, to get normal textures back?

If you installed a body mod, that could be the cause. Most body replacers will use the foot texture for the whole body; but Khajiit feet use the same texture for both sixes, a condition unique to that race; so typically this causes issues with female Khajiit when a female body replacer is used, even if the most recently added body mod is a male replacer.

This seems to be an issue with male Khajits, though.

Please, post your load order.

What use is a load order for a texture problem? Most texture replacers are esp-less - they aren't in your load order at all!

Edit: Sorry, about that. My reply was not helpful or necessary. Anyway, I am also surprised that mail Khajiits are affected because they have their own textures, but I will double-check the Robert Male plugin to be sure.

Edit: Of course, I wouldn't have the plugin installed at the moment...

If using current bash 2.82 there is problem importing mulitpe races mod that change the same thing. For example Slof Better Beast, MaleBodyReplacers, EVE_KhajiitFix with Cobl Races or Race Balancing Project you get vanilla textures instead of Slof Better Beast or MaleBodyReplacer changes or EVE fixes etc.

Best to use tes4edit and carefully copy the stuff from those mods into cobl races or race balancing project until 2.82 if fixed, or go back to previous version of bash 2.77 ..before all the new changes where made.

Corepc

I'm sorry but I have to object here.
Load order or better yet a mod list is crucial for issues with race textures.
We don't even know which bodies the OP is using, if their ESPs are properly placed, if another cosmetics mod is interfering, or if there's a bashed patch so not only the last of all plugins' settings will survive.

The Khajiiti having texture issues with body replacers is a really "historical" trouble.
It all started by the Oblivion.esm giving both sixes of this particular race the same foot texture, the male one.
Then there came body replacers, only using the foot texture for full-body coverage.
Unfortunately some took "replacer" too literally and didn't ship with a proper ESP to fix this Vanilla troublemaker.
Now Robert's Male for example had to avoid messing with these by "not" using a proper "footmale.dds" texture file (overwriting the female textures of the plugin-less body mods) but instead incorporated its own "RTfootmale.dds" only for male Khajiit feet.
Of course now if any body mod's plugin loads after Robert's ESP, the Vanilla settings will be restored, using "footmale.dds" (a.k.a. the female textures) on males.
On the other hand there are female body mods with plugins fixing this trouble by assigning the proper "footfemale.dds" for female Khajiit feet while for male feet keeping the Vanilla "footmale.dds".

There's a hell of a lot of probability for conflicts of this kind and without a list of at least body and cosmetics mods we don't have a chance to "guess" our way to a solution.

Additionally, rereading the OP, we don't even know if the issues occur when nvde (not wearing anything, body replacers alone are in control) or when clothed (body comes from clothing, without proper replacers will revert body back to Vanilla, body mods' textures won't fit anymore, all imaginable issues up to disappearing bodyparts can occur).
Again, without a list of what's in use, we can't know that.

My first "guess" would be: Robert's Male Body in use, some plugin afterwards redirects Khajiit textures, ending up with Vanilla textures on Robert's Male bodies, which is "known" to cause disappearing bodyparts... I just still couldn't figure out why this even happens then in the first place, but apparently, and empirically proven, it does.
edit: Uhm, sorry, there was no "disappearing" in the OP... but all other kinds of texture issues can occur as well then of course.

...well said...