oil leaking from exhaust 95 accord vtec

There is oil dripping, not only soot, but a little puddle of oil from the exhaust pipes where I park. Other than that the car was running great until yesterday when a bunch of coolant got blown all over the
engine. The engine was sluggish after there was a coolant blow out which would be expected.
Today I filled up the radiator with water and idled the engine, water gushed from the radiator. Then stopped the engine and idled it again, and the coolant system never pressurized after running 20 mins two times consecutively. Water never leaked out of the radiator again. While idling, the engine never overheated and maintained normal operating temperature, the thermostat never opened even with the heat blowing for the 20 mins.
I'm pretty sure it needs a radiator and thermostat because the hoses look good. hopefully the water pump is ok. But I have never seen oil come out of the tail pipes on any car. It seems to be pure oil with no coolant in it. ANY IDEAS......KEV
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