Oil engine oil mix with water

Oil is pumped around the engine. If there is water in the oil, that too is pumped around the engine.
If the engine is water cooled, I would remove the head, if it is warped, have it skimmed and then refit with a new gasket.
If it is air cooled, condensation is common. Replace the oil and any filter.

This article says it is from the oil cooler heat exchanger.

http://www.teamfiat.com/threads/engine-oil-mixed-with-coolant.15125/

https://www.google.com/search?q=Tata+indica+vista+oil+mixing+with+coolant

Assuming you didn't pour the oil or the coolant in the wrong filler hole, usually if water and oil are mixing the most likely reason is a head gasket. Did you re-check ALL your bolt torque settings were correct before you finished reinstalling the engine?

could be head gasket
could be cavitation holes in the housing behind the water pump impeller
with no make model year or engine type it is difficult to answer
If it is a nissan diesel that has an oil cooler on the side of the block , they have a habit of failing allowing the coolant to mix with the oil

The only place, oil and water share a gasket is the cylinder head gasket, oil and water galleries run through the engine block and head via the head gasket. The cylinder pressure will be OK, it's the oil pressure that's putting the oil in the coolant, the gasket has gone between the water and oil galleries or there is an internal crack (unlikely). A coolant pressure test should show it up.

Hi Marsha, Many people mix brands of oil specified for either petrol engines and the same is true for oils specified for diesel engines if topping up, but it's not a good idea....It is a very bad idea to use an oil specified for one type of engine in the other. I would suggest never mixing oil manufactured for a diesel engine in a petrol engine or visa versa. The reason is that the diesel engine is dirtier than a petrol engine and manufactures of oil formulate it to have more cleaning chemicals than that used in petrol engines....Mixing the two can result in a build up of sludge which can actually block the lubrication system of the engine causing in some cases severe damage. Regards John

If no external leak and the transmission fluid colour looks white, the problem belongs to the automatic gearbox oil cooler. The oil cooler has broke mixing the gearbox oil and coolant causing this milkshake. It's a small radiator core type oil / water heat exchanger. It is cracked inside and transmission oil is mixed with engine coolant. Because the transmission oil pressure is greater than engine coolant pressure, the transmission fluid level drops. See also the coolant colour inside recovery coolant reservoir inder bonnet! It could be like this:


The automatic gearbox oil cooler type oil / water heat exchanger (oil cooler):


In the picture above the transmission oil pan was removed for oil filter replacement.

If the engine has been flushed well including the radiator and you are still getting water in the oil. The culprit is the cylinder head or the block has a crack internally allowing water into the oil.

The information you gave gives the impression that the head gasket has gone bad and the engine needs to be rebuilt. You can just replace the head gasket, but that's just a quick fix for now. The antifreeze mixed with the engine oil is bad, Antifreeze is very corrosive to the main crank shaft bearing and most likely need to be addressed. At this point might as well go through the whole engine since it's apart. Sorry for the bad news friend. 

the transmission oil cooler is on the lower part of the radiator. it might have a hole inside. you need to replace the radiator and flush the transmission fluid several times