Cashews are high in unsaturated fat, which is exactly what makes them go rancid if stored carelessly. Three things cause the damage: oxygen, heat and moisture.
Airtight, always
Transfer cashews to a glass jar or a good sealed container as soon as you open the pack. A folded-over pouch is not airtight, and exposed cashews pick up staleness within a couple of weeks.
Cool and dark
Heat accelerates the oxidation that turns fats rancid. A cupboard away from the stove is fine; the shelf directly above it is not. Sunlight does the same damage, so clear containers belong inside a cupboard rather than on a counter.
Refrigerate after opening
In Indian conditions, particularly through summer and monsoon, refrigeration makes a real difference. Sealed properly, refrigerated cashews hold their quality for around six months, against two to three months in a warm cupboard.
Freezing for the long term
Cashews freeze well for up to a year with no meaningful loss of texture. Freeze in portions so you are not thawing the whole lot repeatedly, and let a portion come to room temperature in its sealed container before opening — otherwise condensation forms on cold kernels and introduces exactly the moisture you were avoiding.
Keep them away from strong smells
Cashews absorb odours readily. Stored next to onions, garlic, masalas or coffee, they will taste of them. This is the most common cause of "off" cashews that have not actually gone rancid at all.
Telling stale from spoiled
Fresh cashews smell faintly sweet and snap cleanly. Rancid ones smell sharp, like old oil or paint, and taste bitter. Rancidity is a quality problem rather than a safety emergency, but the taste is unpleasant enough that there is no reason to persist. Visible mould or a damp, soft texture means discard the lot.
Roasted and salted keep less well
Roasting starts the oxidation process, and salt draws moisture. Buy these in quantities you will finish within a few weeks rather than stocking up.