So I was visiting friends for a week down in Galveston and obviously I had to bring a few puzzles. Long story short, a ferret managed to knock over a glass of tea and my 7x7 sat in the puddle for I don't know how long because we were out doing things.
Now, a few days later, it's still horribly sticky when I turn it. I'm really loathing taking apart the whole thing and cleaning each piece. Are there any other methods of cleaning big puzzles that I am unaware of?

You'll have to take apart and clean with it with a toothbrush and some warm soapy water,you might have to replace the stickers.

Was it tea with sugar in it?

(else I wouldn't expect it to turn out becoming so sticky)

I would leave it a while in warm soapy water, maybe it will be clean without taking the puzzle apart.

Not a good idea to put the core in the water to just take it a part (you may want to remove your stickers, and after replace them), and give it a good bath, witha tooth brush .

Yes, it was sweet tea.

Thanks for the ideas guys, I guess I will have to end up taking it apart. Darn why can't we live a litter further in the future where a robot could do this for me?

It's likely you will need to take it apart but try this first. Wipe over the outside with a damp slightly soapy cloth. Now quickly run it under a tap for just a second or two and wipe immediately. Repeat if necessary. Now make a few 45 deg turns and wipe those internal faces. Turn and wipe repeatedly for a few minutes.
Obviously what you are trying to achieve is washing the outside and a bit of the inside too with the least amount of water penetrating the puzzle. Note that the corners are part open so check these areas and dry with tissue if they are still wet.

This is a good way to clean the surface of your puzzle:
http://www.youtube.com/watch?v=BP9iZX4dvCU
Video by Tony Fisher

I'll have to try this tonight. I'm sure it didn't penetrate too deeply into the mechanism so cleaning the exposed 45° turn areas just might do the trick. If not, I may have to resort to what Oliver suggested

This should work, provided the stickers are vinyl/plastic and not paper:

1. Quickly turn the layers under a running COLD water tap for 30-60 seconds.
2. Remove excess water by banging gently onto a towel, and/or using your arm as a centrifuge.
3. Turn the layers under a COOL/luke-warm blow drier, repeat step 2 if necessary.
4. Leave outside overnight in the open air (under cover in case of rain).

IMPORTANT: Make sure the water is cold and the blow drier is no warmer than body temp, so that the glue under the stickers doesn't melt.

Hope that helps.

A 7x7x7 has a lot of pieces but it isn't a Petaminx Taking it apart (1 minute?) and putting it back together (15 minutes?) isn't a huge deal, and probably far better than trying a bunch of other half way attempts that take as much time but might not work.

The stickers should be fine in mild soapy water (they are vinyl) so take it apart, soak the pieces (but not the core) in soapy water, rinse, leave to air dry over night. Wipe down the core by hand, and re-assemble in the morning. You may want to re-lube it at this point.

Enjoy your new, clean, lubed puzzle!

Dave