A follow-up for folks reading the ever-scintillating heating oil thread.
I learned from our landlord that the oil tank capacity is 935 litres. The recent fills were 351.3 litres and 423.5 litres. The tank wasn't empty, but the oil company doesn't let you get more than half-empty in the winter. So we actually had not drained the tank in three weeks, which would have indeed been alarming.
The landlord also had the furnace and tank checked just before we moved in. They were given an 84% efficiency rating, which is considered excellent:
Below 70% Wasteful Condition
So, we'll see if we can tighten things up at all: weather-stripping on the doors and sealing up the attic entrance are two likely culprits. And we might be able to decrease our night-time temperature a little. Other than that, the moral of the story is: oil heat is expensive. The end.