Also have you replaced that 02 sensor since the oil burning?
EXHAUST BACKPRESSURE CHECKS
To diagnose a plugged catalytic converter, you can check intake vacuum or exhaust backpressure. To check intake vacuum, connect a vacuum gauge to a vacuum port on the intake manifold. Start the engine and note the vacuum reading at idle. Then increase engine speed to about 2,500 rpm and hold steady. Normal vacuum at idle for most engines should be 18 to 22 inches Hg. When the engine speed is increased there should be a momentary drop in vacuum before it returns to within a couple of inches of the idle reading. If the vacuum reading is lower than normal and/or continues to drop as the engine runs, it probably indicates a buildup of backpressure in the exhaust. Remember, though, that intake vacuum can also be affected by retarded ignition timing and valve timing. What's more, some engines are much more sensitive to small changes in intake vacuum than others, so checking backpressure rather than intake vacuum may give you a better indication of what's going on.
Nice!http://www.aa1car.com/library/converter.htm
In other words, engine can't expel exhaust, it can't ingest air either, so decreased vacuum.
Also notes how to test backpressure, but IMO that's more difficult unless you've already got the gauge and a fitting that will adapt to the O2 sensor hole.

One thing you might want to look for is that the wiring harness, running down the driver side frame rail, is not rubbing against the frame rail and grounding out. Thus causing all kinds of fault codes to trigger.
GM trucks in your trucks year range where known for this. I had two of them with this problem. I cured the problem by just throwing some new wire shielding on the wire loom running from the firewall junction block, and down the side driver side frame rail.
According to my *91* R/V wiring diagram, the tan wire (O2 low/ground) is a separate wire all the way to the ring terminal. Fuel pump relay ground and ECM ground are also terminated at this ring terminal however, so it's not really separate. If the ring terminal wasn't hooked up or the terminal corroded then you'd have problems with those as well.