choose your brand then find their office, then call them up to ask for an authorised jobber address.
e.g. there is a Caltex jobber in lines area Karachi who sell hundreds of barrels of oil a day, buy from them - they would also sometimes have other botique brands like LM etc. You can even buy some fast moving mineral oils from the drum by the litre - Havoline motor oil, formula, delo, delo silver, delo gold etc. quite cheaper that way.
The business is called Mohmand Agency oil trading and is right besides the bridge that is across FTC on Shahrah-e-Faisal - near the military workshop, same road where there was a MAKRO store.