All I could afford wrote:
On my 2003 international 4300 truck, we had a similar problem. Truck was going thru about 3 quarts of oil per hour of run time! Fuel in tank was turning black. Turns out some part in the high pressure fuel system was malfunctioning. Since the oil pressure is used in the fuel pump, oil was crossing over into the fuel return to tank. I forget exactly which part failed.
This is also likely, most fuel pumps have a drive gear in contact with oil giving oil a path to the fuel pump.
Oil have trace of carbon in it? Go to a Cummins or a truck shop and have them to a fuel sample test, they can tell you what's in the fuel.
What year is the ISC? Some are internal with fuel pressure being in the head and some have lines going from the pump to each injector. Ether way it sounds like oil in the fuel, it's not unheard of.
During my past time at Cummins, we had at least one job a day replacing injector Orings.