How to care for a finished item.
Avoid contact with water or other liquids. So a wooden vase is intended as an ornament in its own right or could be used for dried flowers - it is not meant to be filled with water!
Direct sunlight will fade the natural colours in the wood so is best avoided.
Wax finish
A wax finish tends to dull with handling. It will also be affected by moisture - which should be dried off as quickly as possible if water comes into contact with the surface.
Re-apply a good quality furniture paste wax (not a spray wax) and follow the manufacturers instructions.
Furniture polish is generally not edible so a wax finish is not considered "food safe". However you can treat it like you would a polished table so, for example, I would be happy to store fruit that was going to be peeled in a waxed bowl.
Oil finsh
An oil finish gets better with age and handling - as long as hands are dry. As with a wax finish if water gets onto the surface dry it off as quickly as possible.
You can apply more oil every few months and the finish will just getter better and better. I would use a good quality edible oil like walnut oil (which doesn't go rancid!). Apply the oil sparingly using a paper towel or tissue and then after a few minutes polish the surface with a another clean paper towl or tissue. Be careful where you place a newly oiled item as it might leave a "ring" of oil onto what ever it is sitting on!
As long as you use an edible oil then it is safe use the item to store (dry) food, eg fruit.
Danish Oil finish
Danish oil is a commercial product that is a mixture of solvents and oils. It aims to penetrate into the wood (like oil does) while also adding a protective layer to the wood. The resultant finsh has some resistance to moisture and staining - however you should still wipe off spills as soon as possible with a very slightly damp cloth.
A danish oil finish can be re-juvinated by adding another layer of danish oil (follow the instructions on the tin). However if you add too many layers the surface may become glossy and not much different from varnish (which personally I dislike because you can't feel the wood).
You can apply wax to a danish oil finish. However, once you have done this you cannot then go back to applying more danish oil - you have to treat it like a wax finish from then on.
I don't think a Danish oil finish is safe for food, treat it as for a wax finish.
Disasters
If you have a disaster, for example some fruit gets left in a bowl and goes rotten allowing the juices to soak into the wood, here's what to do:
Get some grade 0000 steel wool (www.axminster.co.uk sells this if you can't get it at your local DIY shop) and rub wax or oil (depending on the existing finish) into the damaged area. It will not take any colouration out but it will get the surface back to a reasonable state hopefully. Thats about all you can do - you just have to treat the bowl like an old friend from then on!