To start with, what's the best mod out there to fix all the freakishly ugly NPCs?
Tamriel NPCs Revamped is my favorite, and it definitely covers the most NPCs, but there are other options if you're looking just to beautify females. Also, if you like anime-style stuff, check out XEO. I personally don't know too much about that, though. Read my discussion and watch my video of TNR in action http://matthewkaine.blogspot.com/2011/03/tamriel-npcs-revamped.html.
If so, can someone link me a good explanation of the right way to merge these mods?
Using a Bashed Patch with Wrye Bash should fix most incompatibilities between cosmetic mods, provided you installed everything in the right order and the plugin files are pre-marked with the appropriate Bash tags (they probably are). You can find Wrye Bash and incredibly detailed instructions on how to install at http://tesnexus.com/downloads/file.php?id=22368.
...or do clothing mods continue to use the same system as vanilla Oblivion gear?
That one is more accurate. Oblivion clothing should be completely compatible with any body replacer you use. It might look weird if skin is exposed, though, since the original clothing/armor will still be using the default body as a base. Most body replacers come included or have multiple versions of an equipment replacer, though.
I'm completely confused by the relationship between HGEC and Eshme's EyeCandy. Some mods are made for one, some for the other, and at least one mod I want to use requires one of the two but doesn't care which. And they have the same name. Help?
If you want to use one of those, I recommend HGEC. It's most current, therefore more widely supported. The reason why there's confusion between the two is because HGEC is capable of using Eyecandy's textures. That's a good thing, though, so if you find some clothing mod that requires EyeCandy, it won't look too weird being worn by your HGEC character. They are two different body shapes, though HGEC has several different options in terms of customizing the look. The easiest method of getting HGEC is through http://tesnexus.com/downloads/file.php?id=24078, which comes with its own clothing/armor replacer.
Any mods that get my character out of all those skirts and into something she can fight in would be much appreciated. I had Clothing Freedom, but it was incomplete and won't work with body and clothing replacers. Any other recs of clothing mods that look like they belong in the game would be great, too.
Though I've never personally used this, you could get http://tesnexus.com/downloads/file.php?id=37451, which would be compatible with the body replacer I mentioned above and would get rid of skirts with clothing. It says it includes a new Iron lower body, but there aren't any screenshots of it. Just be sure to install this one after EVE.
And finally! What are some quest mods with good voice acting, and your favorite inventive and visually appealing dungeons?
Other people will have better suggestions for this one, but the largest mod to have both of those things is a Total Conversion mod by the name of Nehrim. It's obviously incompatible with a lot of the stuff I've already mentioned, but you still might be interested. A lot of people have said it was what Oblivion should have been like. I personally prefer just modding Oblivion, but there are others that don't care as much about the lore and such. You can find more about that http://nehrim.de/indexEV.html.
Hope I helped, and welcome back!