Walnuts are, apparently, more susceptible to rancidity than other nuts, because they contain high levels of triple unsaturated linolenic acid, so are best stored in an airtight container in the fridge.
Pickled walnuts, which you mention, used to be an old Christmas favourite, but walnuts can be eaten be raw. AFAIK, pickled walnuts are made from unripe walnuts before they're ready for eating.
However, having said you can eat them raw, too many raw nuts can upset your digestion. They contain enzyme inhibitors, which interfere with it. Try to live off them, as people have, and you get nauseous.
The Aztecs used to soak some types of seeds that they ate - pumpkin, squash - in brine and then sun-dry them. That deals with the problem. In North America the Indians soaked pecans for the same reason. A similar technique can be used with most seeds and nuts, and that makes them more digestible and their nutrients more readily available.
You mix 4 cups (the large 8 fl. oz. cups) of nuts (such as walnuts broken into halves) with a teaspoon of seasalt and some water and leave for at least 7 hours (or overnight). Drain them. You can then dry them in a dehydrator or spread them on a steel baking sheet in a very low oven, turning them now and them till they're dry (takes 12 to 24 hours). Then they should go in an airtight container.