Oil in water

If you have a auto it may be transmission oil from the oil cooler in the radiator. Having changed the radiator may have removed the original fault but there would be still ,oil in the coolant system that is still coming out. Have the system professionally flushed by a reputable radiator shop and then have the cooler tested in the radiator.

check your oil dip stick and see if there is water on it if not sounds like a head gasket leak

it depends on the amount of oil which is left in there

Coolant is oil based. The oily mess in the overflow could be very old coolant. Or it could be engine oil from a leaking head gasket.
The rusty stuff on the floor inside the car could be from a leaking heater core.

What kind of wet? Is the wetness gas, oil, or water? There are different types of fouling possible with reading the color of the old plug being a good indicator. Is the compression within limits?

Check your intake manifold by taking it off and comparing the ports going into the head. If the intake port on #4 cylinder is wet there may be a problem in the Intake. You will also be able to look at the intake valve stems on most motors. The newer designs have the water going into the block directly so the Intake contains no water.

You could have a bad oil seal on the valve stem. You could have a head gasket leak. Even some oil rings can still sling oil and if the power rings are good, it still will compress and give good readings.

You need to run the motor again and try wiping the plug again to see what kind of deposit is on it.

PERFORM AN ELIMINATION OF ENGINE FLIUD CONTAINERS TO ACQUIRE THE TRANSMISION CHAMBER

The vehicle should only have an engine oil compartment, radiation compartment for antifreeze/ water, power steering fliuds, a water wiper blade spray dispenser compartment, and finally the transmittion fliud container area all situted within the engine entrapment area. Usually, opening the engine for the first time would require observing the fliud compartments that are identifyable from the remaining engine chambers. Observing closely on the fliud container should have written descriptions of what is expected within compartment. For example, the water fliud containers for wiper blades would usually have written lables as wiper blade fliud container, radiantion container would usually have the antifreeze demarkation logos visibly observable when engine is opened. Rely by elimination methods to ascertain the transmission fliud compartment. For example, once antifreze container, wiper water container, engine oild container, power steering fliud containers have been identified, the most like only remaining in the engine would be the transmition fliud compartment. Alternately, every fliud container within the vehicle engine is situated at separate areas. For example, the only fliud container closest to the transmittion chamber is the engine oil compartment. The vehicles usually require more engine oil than transmission fliud. Between both fliud containers, the smallest chamber for fliud oil is usually for transmission perposes in the absence of hydraulic fliud compartments with newer vehicles.

If there is water in the oil, yes it most likely a head gasket/cracked head/block problem. Check the oil level on the dipstick. Is the oil level indicated too high? Drain the oil completely into a clear container and let it set overnight and see if water separates out from the oil. The white gunk is a sign of moisture in the crankcase. Short driving trips may cause this also as the motor doesn't get warm enough to evaporate the normal moisture out of the oil.

That brownish color is caused by oxidation(rust) of the waterways in the engine block. Dont worry, your engine wont rust through. This is normal on any car. Just flush it out until the water runs clear. Refill with water and use a good antifreeze as well as it contains rust inhibitors.

sorry to be the messenger of bad news but from the symptoms described it sounds like the head gasket ,the oil feed to the camshaft to be more precise ,its forcing oil into the water circuit but the water is not getting into the oil because its at a lower pressure .

I would have the fluid tested to be sure it contains oil before going any further.