How can I repair water-damaged hardwood countertops?
I'd really need to see a photo to know, but more or less...

A lot of your options aren't great for food prep surfaces: for a non-food surface, I'd use turpentine or Restor-a-Finish.

Start with baking soda, warm water and a green scrubber to get the gumminess up. You might try washing soda or dish detergent if the baking soda alone doesn't do it. Fill a small bucket with warm water, sprinkle some baking soda down, scrub it up, wipe it up with a wet dishcloth, rinse the dish cloth, repeat. I've heard you can alternately use white vinegar. You probably won't scratch the wood but it never hurts to go with the grain instead of in circles. 

Either way, don't leave standing water on the counter, clean it up as you go. 

If it is really nasty you might wind up with a few rinses. Once you get it clean, oil it with mineral oil or refinish it.  If you go the mineral oil route, you pour a small amount on (small) and rub it in (with the grain) and repeat.

UPDATE: I just happened upon a blog post which suggests that a bowl of hot water, a few tablespoons of  murphy's oil soap and a pad of steel wool will go along way. With steelwool and sand paper you definitely want to go with the grain, always. Never ever go in circles. Add the soap to your hot water, scrub with the grain, rinsing often as you go. Change the water as it gets grimy. Keep some rags handy to dry up with so you aren't leaving standing water. 

As far as the warping goes, you probably can't do much except plane it, is a recipe for making everything worse if you don't know what you're doing. Are you moving soon or just starting to realize you maybe need to be more conscientious?