samstrader:
"I think people are saying you just need to replace the distributor when this happens. Is this correct?"
Yes. The "distributor housing assembly" with the rotating parts and the base of the distributor isn't designed to be disassembled, so if the bushing (and possibly a seal) in it is worn to the point of wobbling, it is likely to leak oil as well. I've never seen one in this condition, but it's reasonable to expect that it could happen in a van that had seen a lot of miles.
"What is the purpose of the two short hoses that are connected to the distributor. I used to think they were cooling water hoses but don't think that now since they are never very hot."
Good question. As you found, these hoses don't carry cooling water, but since there are two of them it's reasonable to imagine that they carry warm air out and cool air in. Since the distributor is just above the exhaust manifold, Toyota's engineers must have been concerned about the distributor getting too hot. The heat shield on the bottom blocks some of the heat being radiated by the manifold, but passing cool air through the housing could help protect the internal parts. Later engines have no distributor at all, but the Previa engine had not evolved to this point - at least not those sold in the US.
It's sad that your dealer laughed at you. I have replaced that plastic hood-prop clip myself. We live in a 'throw-away' culture and they shamed you for wanting to maintain your van. The auto manufacturers want us all to buy new cars every few years. I have found Toyota better than most at making parts available for their older models, but since Previas are around 30 years old now, it is becoming more and more of a challenge. Those crazy-long wiper blades are a good example!