I'm building a bike from scratch at the moment - mainly from
ebay parts... Quite a learning curve but I've got the ear of a local mechanic that can help.
BB cartridges are a mixed bunch, you can get ridiculously cheap ones - or really nice expensive ones. But with them all, oiling is pointless - if it is the BB that's gone, it needs replacing. If oil can get past the seal, then so can water and other road cr*p.
If it's an old fashioned spindle and bearings BB, then it's a simple job to repack and tighten it up - provided you can get the tools.
Alternatively, you might have a modern external bearing BB (with the big exteranal bearing cups screwed onto the outside of the BB). In which case, the face of the BB itself may be a factor too if the bearing is wearing too quick.