Spark plugs covered in oil - how screwed am I?

In addition to what has been said about the plug tubes, etc, make certain that something hasn't happened to "wash" the rings. Maybe the carb needle seat stuck and flooded it bad, maybe the FUEL PUMP is leaking gas into the pan.

I would get good plugs in it, make sure it seems to be running OK, go for a long enough drive and at speed to get it fully warmed up and then monitor the plugs and oil level