Engine overheated and shut down, coolant empty and no oil on dipstick. Added water and it was quickly leaking out of engine somewhere above the oil pan. What is likely cause?

A car that keeps overheating should not be driven.

Light blue smoke is burning engine oil. This is probably a sign that overheating has damaged the engine.

Water pump can leak coolant, make a noise and even wreck the engine under some circumstances but they have little to do with engine oil. If the water pump leaks it is an external leak.

If there are no external coolant leaks then yes it could be the head gasket or perhaps a crack somewhere...

i think you should replace gas kit and give it for service
?taking risk like that can blow your engine

Sounds like you're low on coolant. That's not good, because it being a sealed system, you should never have to add coolant. The level should always stay full. If adding is necessary it is almost certainly leaking somewhere. If you can't see any external leaks on the engine or hoses or radiator, check your oil sump for coolant contamination: pull the oil dipstick and look carefully for milky brown swirls in the oil. That's the color the coolant gets in the oil. Take off the oil filler cap and check there too for a brown sludge. Just precautions because worst case scenario, if that's where your coolant went, it probably means a costly head gasket job.

If it turns out to be low just from neglect, you may be alright, but you need to keep watch on the coolant level for a good 2 weeks or more to be certain it is not losing coolant somewhere. Be sure and bleed the air out of it too, when refilling coolant. I don't think that was what happened, an air lock, as the cause of your overheating, though.

If you have the 2.7L engine, you may have a bad water pump. The water pump is turned by the timing chain. When the water pump on those particular engines go out, tension on the chain goes away and retards the camshafts bad enough for it not wanting to start. Pull your oil dipstick out and see if you see signs of water in the oil. If there is, this is your problem. When the water pump goes out on those engines, it'll drain water straight into the front of the oil pan.

Yet--Hopefully

Head Gasket
Intake Gasket
Water Pump & drying off so you don't see it

I'd watch to make sure water isn't getting into your oil.
If it overheated, a head gasket or warped head could allow water into the oil pan.

Water would seem to mysteriously go away.
Just make sure after adding lots of water that oil on the dipstick doesn't look like a chocolate malt.

Otherwise, a leak is somewhere else.
Heater cores, water pumps, and radiators need to be looked over for hairline leaks.

As more and more water has to be added to keep levels correct...problem will show itself soon.

Hope this helps...

milky oil would suggest water has mixed in with it. this added to a slow, unfound water leak points toward a head gasket problem with the coolant escaping from the cooling system, into the oil.
this needs to be sorted out fairly quickly. apart from the obvious problems of a water leak and the risk of overheating, oil with water in it will not lubricate the engine properly and there is a serious risk of engine seizure.
a garage should be able to do a simple test on the oil to discover if it is coolant contaminating the oil.
a pressure test on the cooling system would also confirm where the coolant is being lost.

Need to seal the leak in the coolant container with epoxy or by replacing the coolant container.

Fill coolant system with 50/50 solution up to 2 gallons may be required to stop the overheating.

Don't drive an overheated engine.

its under the throttle body near the coil pack

I had the same problem on a Vauxhall Montery (Same Car), The thermostat jams shut thus causing the engine to overheat and damages both the cylinder head and gasket, first thing to check is the enigne oil, pull out the dipstick and check for a white, spongy liquid. If present then your head gasket is passing water into the crankcase, If engine oil OK then fill up the coolant system and give the car a good old rev for a few minutes then check teh exhaust for water. In both cases the cylinder had needs to be removed, skimmed, gasket replaced and thermostat replaced.