So I assume you are sure that it is not leaking oil rather than burning? If it's burning that much oil, that's a little scary. If that continues you could experience "runaway diesel" one of these days. If you don't know, that's a condition where so much oil from the crankcase is bypassing the pistons that it feeds the combustion chamber in an uncontrolled manner and the engine revvs out of control until it self-destructs!
In that situation turning off the ignition key, fuel cut-off, hitting the brakes, all will be useless - the only way to avert disaster is to manually block the air intake by stuffing something like a folded blanket into it or a flat object on top of it, depending on how your intake is shaped.
All my diesels get Shell Rotella 15w-40 or Chevron Delo 15w-40. I've tried cheaper oil and regretted it. Some people swear by the Mobile 1 synthetic oil, but that is way too expensive for my budget.