Question

why are solid sodium potassium and lithium stored in kerosene

Answer 1

 Sodium(Na), Potassium (K) and Lithium (Li) does not occur naturally and are highly reactive metals.

Sodium(Na) and Potassium (K) quickly undergoes reaction with air or H2O (water or moisture) and burn violently and can explode, so it must be stored in an inert medium such as an inert liquid hydrocarbon (example: kerosene) as moisture cannot enter in it. 

whereas, Lithium (Li) is an extremely volatile metal and kerosene is too a volatile liquid, if stored can float on kerosene and get exposed to air which can cause explosion so it is stored in paraffin wax.