I write way too much dialogue.
For accents, you really shouldn't be forcing accents in a book unless you're very good at it or the character has a VERY distinctive and very pronounced accent. If you're writing about somebody with a (stereotypical) Transylvanian accent that causes them to say their v's as w's, you don't have to write:
"Ven are ve going to get there?" Said the Count
You could write:
"When are we going to get there?" Said the Count. Thanks to his thick Eastern European accent, I had to stop and mentally change all the misplaced "v's" back to "w's" before I could figure out his meaning.
Accents in general tend to be one of the things that it's okay to tell instead of show. If you write something like this:
"Ah said ta Puhrl, Ah was fi'in tah gimme sum afore Ah got mah warsh done." (and yes, I know people who speak this way)
People are going to have a hard time reading that. But if instead you just say;
"I said to Pearl, I was fixin' to get me some 'afore I got my wash done." But mention that the character speaks with a hills/Virginia accent (assuming your story is set in the States, if it's not, you'd have to specify), many people will understand what you mean, and the ones that don't won't suffer for not understanding what the heck you're talking about.
The other thing that can help with making dialogues sound convincing you pretty much hit on the head. Slang. You used the examples of an Aussie saying crikey or a New Yorker mentioning the Yankees. Obviously if you want to have a certain person identify with an area, slang is going to be an easy way to do that. I can't really give you a run down on every type of slang used in every English speaking area (mainly because I don't know all of them), but there are websites dedicated to these sorts of things if you look for them. Like this awesome dictionary of British slang:
http://www.peevish.co.uk/slang/index.htm
Or this list of Boston slang:
http://www.aboutlanguageschools.com/language/slang/boston-slang.asp
Just type in "list of .... slang" (with the dots being replaced by the area of interest) and you should be able to figure it out.
As for the actual patterns themselves, once again, there is no hard and fast rule I can give you. But it's always helpful to talk to speakers from whatever area you're going for. There are a lot of websites that have recordings of different accents, so you can listen to different speech patterns that way. With enough practice, you'll probably start noticing the differences. It's all a matter of exposure (for example, I'm originally from Ohio, and anybody there can tell which part of the state you're from by how you say the words "button", "wash", and "bedroom" but if you aren't from Ohio, nobody is going to pick up on that...)
Since I typed this before I saw the edit, I'll add (even though this is insanely long already):
The slang thing holds true for fantasy worlds as well. Most people use slang, and a fantasy world is going to have it's own sorts of slang. Coming up with different terms for the characters to use not only helps to give the world more depth, but it also makes the characters speech more believable.
Also, think about the character's education and background. A more educated character is going to speak very differently then a less educated one. Likewise, two equally educated characters will speak differently based on how they value their education (a character that wants to prove to others he or she is smart will speak in more elevated diction then they would otherwise for example). Using longer words, complex sentences, and precise phrasing can signal to the audience that a character is either better educated or is rather pretentious. Depending.
There is also always verbal tics. I knew a girl once who always ended her sentences with "yeah?" when she was nervous. (ie "We should go this way, yeah?... I don't really think this is a good idea, yeah?") You probably wouldn't want to do something so blatant, but you could try something like that.