Last week, a plumber poured sulfuric acid (Clobber, maybe) down our kitchen sink to unclog it. A few hours later, my wife smelled fumes and said smoke came out of the cabinet underneath the sink when she opened it. The next day, we had a different plumber come by and he said that we should throw out all food, toaster, and coffee pot and not move back into our house until that is done. He also said we need to wipe down all furniture and objects in the house. Does this sound like an appropriate response to acid fumes or are we overreacting?

Yes and no.
Clobber is a very strong acid that must be handled carefully.
The smoke you wife saw is the result of the acid reacting to what ever organic material it came into contact with. If it leaked out of the trap below the sink you need to fix this leak. If you do not have the proper vent and a under sink vent is installed the fumes may have come from that. It should not but its a possibility.

If the acid leaked out from the drain then you do need to carefully clean up the spill.

As far as discarding the stuff below the sink. If is metal and no acid came into contact with the objects you simply need to carefully clean them before you use them again. If they did get wet from the acid then you may want to consider discarding them. But any food product should be thrown out.

As far as wiping the furniture down etc in the house. That sounds like overkill. How much fumes and smoke came out? If it was enough to blow over the furniture etc whowever used the cleaner should have a strong talking to. And quite frankly you would have gotten quite ill fast. You would have to have used a gallon or so and poured it onto the floor and all over the inside the cabinet to get it bad enough to have excessive issues like this.
But because I am not there I cannot tell you if its a real issue or not. Go here are some general guidlines for you to follow.

You need to ventilate the kitchen area well. Wear rubber gloves when doing this to protect your skin. And of course wear eye protection. Flood the area with lots of water to dulute what ever acid remains. Soak the water up with lots of paper towels and throw them into a plastic bag that contains nothing else.

If you have a concern with the acid fumes that may have come into contact with the furniture and other items. Simply wipe them down with a cloth dampend with water.

There is nothing else you can do. As long as nothing has gotten wet from the acid that could not be cleaned or dried and those areas that did were flooded and cleaned with clear water, you should not have to worry anymore.

Just my two cents worth, but instead of cleaning with plain water, use a mixture of baking soda and water. The baking soda solution will bubble when it comes in contact with any acid, whether it is sulfuric acid or vinegar. The bubbling indicates that the acid is being neutralized. When there is no more bubbling, the acid is neutralized. Using plain water will only dilute the acid and possibly spread it over a larger area.

The plumber that used the Clobber failed to flush the lines enough. Sulfuric acid will readily digest metal drain lines if it is left to sit in the line. The comment from the plumber about throwing away food, appliances, etc. is based on ignorance.

It is essential that baking soda be used to clean up any spills/leaks. For wiping down areas that you cannot pour baking soda on, make up a solution using approx. 4 - 6 oz of baking soda in one quart of warm water. Use a spray bottle for hard to reach areas. Apply and rinse until fizzing stops. Follow all safety guidelines as mentioned above, especially goggles. If skin contact occurs rinse the area thoroughly and use the baking soda. If eye contact occurs flush eyes for 15 minutes and see a physician immediately.