You've written "oil jobber", so I'm assuming that this is a company that resells oil to shops and maybe small retailers or convenience stores.
It appears that one of your recommendations as their consultant should be that they put a better inventory control system in place to avoid being in a positon of having large amounts of obsolete inventory.
To the question at hand, I'd recommend selling it off as cheaply as you must just to recover some money from it.
How old is this oil?
Five years, ten years or older?
Many of us have cars originally speced for API SJ or even SG oils, so the spec isn't necessarily a barrier to the oil being sold, it will just need to be priced accordingly.
I'd offer the oil through non-traditional channels, like here and CL.
If the stuff is really old, offer the conventional at a buck a quart and the syn for two.
If it isn't really that old, and it is of known brands, maybe ask fifty percent more.
I'd not offer it to the company's usual customers, since that would cheapen the image of the company and might make the customers think that your client is the go-to vendor for cheap oil, but maybe not for regular stock.