Staining a previously oiled fence
you will have very mixed results applying a stain over any kind of preserving oil.  the preexisting residual oil will prevent stain penetration, and as it weathers further, the old oil will continue to breakdown, leaving areas with none of the new stain.  

you can use tung oil or danish oil (both readily available in bc), but just remember, natural oil finishes essentially need to be redone annually

if you want to convert to a synthetic stain, it will need to be oil based, and you will have to apply 1 or 2 coats of mineral spirits to the wood first to re-dissolve the old oil finish and make it possible for the new oil based stain to saturate into the resulting old oil/mineral spirit solution