Hi Baywitch,
that's two complex question's, my answer isn't neccersarily right or definitive (I'm a newb writer myself) but what the hey, I'll have a go.
I think the ultimate purpose of fleshing out a character (something I struggle with too) is to try and get to the point where your readers stop thinking of them as characters and start thinking of them as people. Which is difficult.
There are lot's of techiniques, and just like everything else in writing, there's no one right answer or one way to do it (unhelpful I know).
I guess the first step is to make sure you're not using stereotypes (the tart with the heart, the strong but silent warrior, etc.) or stock characters (the fat jolly inkeeper for example) as these will always seem stale.
One trick James N. Frey talks about, in "How to Write a Damn Good Novel" is to flip the stereotype on it's head, and go in the opposite direction, by looking at what has gone before in your genre and creating a character that goes against type.
The example he uses is hard boiled detective fiction, where the protags are usually ex-cops/soldiers, terse, tough on the outside (with a soft heart when it comes to women) and good with their fists. He then turns this on its head and creates a detective who is the opposite; an academic type, fast thinking, not pyhiscally strong, but equally determined to solve the case and equally unafraid.
Another technique is this; for each important character do a write up, a page or two, on each of these things; Physiological: all the usual, height weight eyes hair stuff, and more detailed descriptive stuff too. Sociological: social background will make a massive impact on a character, their upbringing, skill set, resources, circle of friends, job, etc. all stem from their social background and finally Psychological: what drives them, fears, passions, defining moments, etc.
Then write a short (again one or two pages) Bio, detailing their life up untill the point your story starts. Write this bio in your charcter's voice in first person (even if you won't be using that POV in your story).
This proccess is one way to flesh out a charcter or a start at least, there are lots of techniques available, whole chapters dedicated to it in how to books and whole books about creating characters.
As to "strong voice", your characters only need be obnoxious , if you want an obnoxious character.
A strong voice is an individual one, a unique one. A voice you can read and know isntantly, this is a particular character or this is a person, an interesting person, one I want to read about.
In first person, a voice has to be really strong as it carries the the story. No matter what the plot, or how interesting/exotic the character might be, if it's delivered in a flat or dull voice, the story won't work.
In third person, the protag's voice won't be so prominent (but you'll need a strong narrator's voice or style) but is still equally important. As an exampe in dialogue you should be able to tell line by line, without any speech tag's which dilaogue is that of your protag's, and which is the other character's.
A strong voice has it's own rythms, nuances, and phrases. Places a character, say a lot about their social standing (a teacher and a janitor will have very different voices) their jobs, their outlook on life.
Err, I'm rambling on now. Voice is really complex, I don't fully understand how to do it, let alone how to explain it.
Here are a couple of links to articles that might help.
Voice...
http://www.poynter.org/content/content_view.asp?id=68795
http://www.rachelsimon.com/wg_voice.htm
Character...
http://www.rachelsimon.com/wg_character.htm
http://www.poynter.org/content/content_view.asp?id=66542
http://www.writerswrite.com/journal/feb00/keegan22.htm
Anyway hope that helps however little.