For some reason, dental care has just as much bogus information as fitness does. This is most likely to make additional profit off of people who don't know any better. As a tip, if you're not interested in why each of these products is nonsense, you can just skim through the heading to make sure you don't fall into any more dental scams.
Activated charcoal
While activated charcoal may help remove surface stains on your teeth [1], there is no evidence that it has any effect on stains below a tooth's enamel or that it has a natural whitening effect.
The reason that it is able to get rid of surface stains is due to its abrasiveness. In fact, it is so abrasive that it can wear down your enamel [1, 2]. A reduction in the enamel will eventually make your teeth look more yellow by exposing the dentin, a calcified yellow tissue, and make your teeth more sensitive.
And because of its black color, activated charcoal can stain your teeth by slipping into the cracks and crevices of older teeth.
In summary, like every item on this page, activated charcoal isn't worth the price and/or the damage it causes.
Kaolin clay
Also known as China clay, this product has no scientifically-backed studies that prove its effectiveness. For chemical compounds that have been shown to work, head over to the 
4. Brushing Well and 
5. Further Whitening pages.
Fruit peels
These can actually whiten your teeth due to their acidic pH levels but at a huge cost. Prolonged use of acidic compounds on your teeth, as discussed on the 4. Brushing Well page, will damage your teeth enamel.
When applied too often or in high quantities, the acid from fruit peels will strip the outer layers of your teeth to expose the sensitive and yellow dentin beneath.
Apple cider vinegar
Like fruit peels, apple cider vinegar (ACV) can potentially whiten your teeth but at the cost of eroding your enamel [1]. Keep in mind that enamel is needed in order to keep your smile looking bright and your teeth healthy!
Lemon juice
Following the same logic behind fruit peels and ACV, lemon juice's acidic nature can whiten your teeth at the cost of eroding your tooth enamel.
Really, the TLDR for any teeth whitening product that is acidic is to stay away from them.
Strawberries
The main reason why strawberries don’t work as teeth whiteners is their chemistry. They don't have any hydrogen peroxide or carbamide peroxide, both of which are key ingredients in tooth-whitening products (as discussed in previous pages). It's a mystery as to why strawberries are considered teeth whiteners as they also aren't particularly acidic.
Wood ash
Wood ash literally comes from your fireplace, a great reason to not put it in your mouth. While it does contain potassium hydroxide (a chemical compound that has whitening properties), it does not have enough to be effective. But that's really beside the point. Don't, in any situation, rub something you burnt in your fireplace on your teeth.
The Perfect Smile