I've checked the oil and there is no coolant in the engine oil but
There is engine oil in the coolant overflow tank

I've seen some post on this and they have changed out one of the oil coolers with success.
I ordered an oil cooler and cannot figure out how replacing this is going to fix the issue.
The oil cooler appears to have a oil input and output---- correct me if I'm wrong but how does the coolant move past the oil here causing this issue for a failed oil cooler?
Should I be looking elsewhere for this failure?

 

Most likely it's a blown head gasket, but without knowing more it's anybody's guess. I wouldn't drive it or start the engine, as that could cause more damage.

If you don't have enough automotive repair knowledge, experience, and tools, your car should be towed or delivered by flatbed to a competent repair facility.

https://mechanicbase.com/coolant/oil-in-coolant-reservoir/
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Could be the oil cooler - not too much in the manual regarding cooling of the oil cooler except this:

22 . Disconnect the coolant hoses from the engine oil cooler.

So it's possible that a corroded oil cooler maybe letting oil in to the coolant system considering the age of the car.

 

On further thought ... we need more information to give you good advice.

1. Does the engine start and run without making any unusual noises? If it's noisy, shut it off and don't restart it.
2. Are any dashboard warnings illuminated?
3. Have you checked for stored DTCs? (Diagnostic Trouble Codes) If not, you must run a scan, write down all the codes, and let us know what they are.

Trying to fix your XK by trial and error is inefficient and wastes time and money. The best way to repair your XK is to use the DTCs and Workshop Manual (see the Sticky Threads).

 

can also be trans fluid contamination

 

Don't get upset. If your head gasket is leaking , the coolant usually ends up in the oil. Not the other way around. You are talking of a small amount of oil. Some junior mechanic may have added some oil to the coolant tank in error.
Change the coolant.
Measure if your oil level drops.
I believe the oil coolers are stand alone, and are not using the radiator for cooling.

 

How about that one kid who filled up the 'windscreen washer' by putting a garden hose into the oil fill hole?

 

Looking in the JPart catalogue - the oil cooler shows only 2 hoses. So there is no way a leak in it would lead to oil in the coolant:

 

On second thought: Since oil is lighter than coolant, just remove the oil from the coolant tank (vacuum hose), and constantly measure oil level in the engine. Leave the level of coolant down an inch or two for the arrival of new oil!

 

Yes the Oil Level when down by about 1/2 capacity when this occurred.
The engine fans stared running fast and I shut it down immediately
Definitely not transmission fluid in coolant just almost all the oil from the engine.

 

If the oil is at halfway down the dipstick that is around half a pint of oil. That's a lot of oil to end up in the
coolant tank which would almost fill it to the brim. Maybe the oil was already low before you noticed it
in the tank?

 

WOW! How can the oil go from its channels into the coolant channels? Where is the breach?

 

I found this solution to a 4.6 liter V8 Ford. The problem was the manifold gasket and this owner solved the problem with a internal liquid sealer. The discussion favored Lucas or BG brands for not blocking passage ways with metal pieces.

"I had the same symptoms with another make that was notorious for the "gold" coolant eating up the plastic manifold gaskets. In my case it was a loss and I just wanted to keep it running. I added engine block sealer and radiator sealer (the kind with copper flakes). Ran it a while. Then I drained the coolant and filled it with water and TSP three or four times to flush the system. I added green coolant and it cleared up almost 100%. It was amazing and didn't have any oil in the reservoir. I drove for a few more years."

. The Ford V8, 4.6L has this problem and it may be the 5.0L, in Jaguar.
Possible manifold gasket not head gasket.
Manifold gaskets are easier to change than head gaskets.