Hi Rich
Not sure on the Aqua Mix HD cleaner.. don't think it will strip oxidised Linseed oil but worth checking to make sure.
But LTP do one that is made for stripping that kind of oil sealer.
LTP Power Stripper
Description:
LTP Power Stripper is one of the few products on the market capable of breaking down oxidised boiled linseed oil from the surface of terracotta. With powerful amines, ammonia and alkalinity that penetrate and help lift the hardest, heaviest films, it is ideal for intensive cleaning of heavily contaminated vitrified quarry tiles, glazed ceramics and porcelain. Strips most things first time thereby minimising labour costs.
Tips: Pick this product if you have heavily soiled surfaces, old layers of sealer, oxidised boiled linseed oil, residual grout on the surface of limestone....
Technical Data Sheet (PDF)
You can order it direct on line from LTP Here >>>
LTP Online | Cleaning Products
As for sealer's stopping damp and effloresence then this won't be possible.. some help to prevent salt formation but not a cure.