What will be the effect of engine oil mixing with water?

Question edited for clarity.

No to both. The water pump is chain driven and takes water from one side and pumps it out under pressure from the other. The thermostat is fully enclosed in a housing with no access to oil.

Oil in Coolant only comes from a failed head gasket where the oil and water channels are in close proximity and under combustion pressure of hundreds of pounds.

Water pumps are designed to pump water through the engine, radiator, and heating system. Water pumps will not cause oil to enter the cooling system.Oct 4, 2016

Q: Can a bad water pump cause water in the oil - YourMechanic

Water Pump
https://shop.advanceautoparts.com/find/nissan-maxima-water-pump

Thermostat Housing
https://www.google.com/search?q=nissan+maxima.+thermostat+housing

..

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

hi there.
Water in the engine - Water can get into your oil sump in two ways: ... Water in the oil- Coolant leak due to non-watertight seal (cylinder head gasket, etc.). If this happens, there is a leak and water is getting into the oil.
Water in engine oil
If you found water in oil car , this water engine car section is for you!
Water in car engine? Water should never be allowed to get into the oil in your engine or gearbox. Otherwise, it will result in significant foaming, dramatically reducing the product's lubrication properties.
Water in the engine - Water can get into your oil sump in two ways:

• Water in car - Water condensation in cold air or combustion gases: this phenomenon is extremely rare and only occurs at specific temperatures.
• Water in the oil - Coolant leak due to non-watertight seal (cylinder head gasket, etc.). If this happens, there is a leak and water is getting into the oil.

Water in motor oil can cause serious damage to your engine - the oil will be denatured and no longer effectively cooled.
Contact your repair centre as soon as possible.

Um, most likely not good. Most likely means the block is cracked allowing the water and oil to mix. Major engine repair.

...

Water coming from the overflow bottle usually means excess pressure in the water system or a faulty pressure cap. The first can be a failing head gasket, the second is a cheap fix. Taking the thermostat out will have no effect on water loss but will have a big effect on cooling. If you remove the thermostat the water circulates too fast through the rad and overheating results. You need to find someone who can properly pressure test the cooling system to arrive at a suitable answer. Have you removed the dipstick? Has it a white sludge on it? Is the engine oil discoloured to brown with white traces? If so then a head gasket is likely. If you've run it for any time without the correct coolant mix then its likely internal corrosion has eaten the gasket. When all is fixed run the correct mix.

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.

If it is transmission fluid it is likely the heat exchanger (or cooler) has sprung a leak. The cooler is often integrated into the main radiator bottom tank. If fluid is entering the cooling system it is possible coolant could be entering the transmission.

Tranny fluid will appear clean and floating on the surface of the coolant and is likely to be pink or red while if it is engine oil it will be an altogether dirtier colour and more viscous. Try capturing a sample with some clean white tissue when the engine is cold.

Engine oil in the coolant could be a sign of a failing cylinder head gasket.
A failing head gasket is likely to produce unusual cooling system symptoms including ejecting coolant from the reservoir while a leaky tranny oil cooler is unlikely to have much effect on cooling system behaviour except for the obvious...

you need to find that leak, is the leak visible? if its not from radiator or the reservoir, the only other place I could think you can lose water is the head gasket. It happens to high miles and hard driver. 100k miles would likely be a head gasket. Leaking head gasket will also cause the engine temperature to rise and run super hot. antifreeze will leak through the head gasket down to your oil pan mixing oil and water. Check your oil by pulling the dip stick and see if you have oil mix with water; it will have a slimy looking colors, oil is light color and it should never be black. if it black than change your oil and inspect it afterward when the car has been running for while. when engine really hot cause the heat to effect the starter not to engage or start or engine is too hot to run. repairing head gasket could run anywere from 500-800 bucks.

If it was not overheated real bad the intake gaskets are a big problem on those engines

The oil will appear 'milky' if water mixes with it.