Can I just move the entire Oblivion folder (mods, expansion, and saved games) to my external hard drive, reformat my PC then transfer it back or will that mess up the registry?

That will almost work.

Do exactly that, but, before you copy everything back over, Install the game, if you have GOTY edition, install SI and KotN as well. Once you have the game completely installed that way, just copy your back over, and simply overwrite everything. Should work fine.

Might not work for assorted utilities though, (Wrye Bash, OBMM, et.) might end up having to manually reinstall those. Not sure. Try it and see.