The reference is to the murder of Thorin's grandfather Thror a few paragraphs earlier:
"Your grandfather Thror was killed, you remember, in the mines of Moria by Azog the Goblin."
So when Thorin says "We have long ago paid the goblins of Moria", he is speaking of revenge. The modern idiom (in American English, anyway) would be "We long ago paid back the ...
He means that they metaphorically "paid back" (i.e. took revenge upon) the goblins for their role in Thror's death. At the Battle of Azanulbizar, where Thorin earned his name "Oakenshield" and his cousin Dain slew Azog the goblin king, the dwarves exacted their vengeance for the murder of the king of the Longbeards.
Per Tolkien Gateway:
The War of the ...
Wine, and lots of it. Also beef and butter. From the description of the Elvenking's realm in The Hobbit:
There stood barrels, and barrels, and barrels; for the Wood-elves, and especially their king, were very fond of wine, though no vines grew in those parts. The wine, and other goods, were brought from far away, from their kinsfolk in the South, or from ...
I find it has a dual purpose of a nod to Hollywood history, and to elicit a smile and a chuckle (to those in the know) without breaking narrative during otherwise sombre and tense moments. Anyone complaining about it is really just bragging about recognizing it.
If you're looking for a picture book, there's a 1999 graphic novel you could look for. Otherwise there are a various illustrated editions that might be appropriate for reading along with; I found a list that includes several of them.
Apparently there's even been a pop-up book, though it's not the complete story.
Yes, several abridged versions have been made available;
The (2009) Highbridge Radio Edit (full cast)
The (2002) BBC Radio Edit (full cast)
The (1993) Martin Shaw Abridged Audiobook
The (1986) BBC Radio Edit (full cast)
The (1979) Jackanory Radio Edit
The (1964) Princess Magazine Serialisation ( http://www.tolkienlibrary.com/tolkien-book-store/PC000007.htm)