You could include chess pieces and playing cards as part of your centerpieces or favors, sticking to the theme colours of black white and red.
For example you could make a tower of cards all glued together as a centerpiece for one table and then on another have a chess board with the pieces arranged in a love heart shape.
You could also serve oysters as your entree (from tweedle dee and dum's story) - but be careful because they are an aquired taste and many people aren't very open minded about seafood.
You could include quotes from the book "the time has come the walrus said to talk of many things..." etc on the back of the name cards - which could be made out of playing cards.
Have outrageous tea cups and saucers as favors for the women (ala mad hatters tea party).
There are a new style of wedding cake called the mad hatter which are all wonky and crooked and look fantastically unique and can be made as zany or as plain as you would like which would really suit your theme too. Have a look at the link below.
http://www.uniquecakesbykaryn.com/wedding-cakes/mad-hatter1.jpg
The disney animation has the queen of hearts carrying a 'sceptor' which could be emulated by using red heart shape lolly pop favors tied with a pretty ribbon. The plus side of these is that they're cheap and tasty!
Hope you find some inspiration and have a wonderful day!