There's almost no possible way oil can get in the heater box to smell like burnt oil; I doubt it's oil. BUT, the blower motor and/or resistor can be going bad and causing this burning smell. In the MJ years the resistor is usually the issue, but it may be worth replacing both while you're at it. If you don't (best case) the blower motor will stop, or (worst case) you could have an interior fire caused from the resistance of the heating/shorting out of the wires.
Here's a YouTube video of a resistor placement of what looks like a right-hand drive diesel XJ: