If I had to compare the dialect with a historical dialect, I would say it is probably nearest to the language of Johnathan Swift and his contemporaries, although Sanctuary has sort of developed its own kind of dialects.
In Upper, it's like...
"Say, stranger, how about lending me a hand with this cart? I don't know if I can get it all the way to Serena Tower alone."
Lower,
"Oi', I can' get this damned cart on an' o'er the bump o'er here. Mind given'er a tug'er two t'see if we can't straighten the little sunuvabitch out, eh bloke?" (Maybe a bit heavy accented, but things are cut off more. Too much, like this, can sometimes be overbearing and frustrating to read.)
In the sewers, it's like...
"Rest, yis for five shinies! Wheeee!"
-Noogak Boogleman, goblin merchant
Then you've got the typical dwarf-Scottish voices, although these aren't required nor are they held to be particularly canon as far as I know. I do know that they are easily overdone, so be careful!
Elves don't really have a special "voice". They might use flowery language, since they're used to long words like Tel'Quissara.
Halforcs are voiced "Lika diz. Likez da shinies!" a lot, which is IMO far too common and quite frustrating. Half orcs don't have to be mentally retarded with 18-20 strength all the time, but that's a whole 'nother can of worms.
Gnomes tend to be excitable and love fancy words, but speak normally otherwise.
Halflings are lighthearted, not to be confused with infantile or overbearingly childish. They can also be very serious though, staunch nearly, as most halflings, canonically speaking, are lawful. Their pantheon reflects this (3 LGs, 2 NN, 1 LN).
Of course, Sanctuary is a town of ex slaves from a hodgepodge of different backgrounds, so voicing is going to be diverse.
Some EfU/Sanctuary only things, as you have probably noticed and hopefully others will add to. The reasons for the changes are usually because the old word is non-existant or far too uncommon in the Underdark for common folks to recognize them and thus are changed to their Underdark subsitute.
Today/Tonight=Todark (They'll be leaving todark.)Day/Night=Dark (Fair Dark!)
Underdark=Dark (The Dark is a dangerous place, don't forget to take a towel.) This is occasionally put as 'Dark to represent the shortening.
Bull=Rothe (That's a load of rotheshit.)
Fox=Rat (He's a cunning rat, that one.) Not necessarily negative, although it still is typically.
Wood=Zurkh, Zurkhpulp, Zurkhwood (Gee, his arms are a carved like zurkh.)