Oil in a coolant, lots of it got out somehow and flooded coolant tank, i got a lot of smoke or steam coming out and some smell of petrol in a car. there was no heating working in a car just before the problem started. what does it mean? rover 25, 1.4 petrol, 56000 miles

I moved you from computers to cars, its not computer ok>?
and no CAR stated, no model stated
My guess is you damaged the oil pan or transmission pan.
in USA we call it a pan and not sump that is British jargon.
we'd call a hump in USA a bump or a speed bump or a huge CHUCK hole (as in wood cuck made)
or did this OFFROAD, (done lots of that me wheeling/cycles)
there are 3 kinds of smoke
1: black/gray dark , rich fuel mix.
2: white /blue tint ,smells like burning oil and is, and slow to dissipate.
3: white pure, steam, steam here, is water from coolant,
an goes away fast , and smells sweet ,just like antifreezes smells.
so the word smoke tells me nothing but is a problem.
what no take car to shop and ask? be wise and most safe.
to you and even the car.

nor any photo of damage under car posted.
we can't drive your car and see smoke .so.......
ask your shop why. is best.

Water in the gasoline, or a leaking head gasket. A leaking gasket may not show water foaming or discoloration in the oil, but level in the radiator will go down over time.

Are you losing coolant?

the HONDA Horizon (Isuzu wonder box)
what engine. exactly .?
3.2 L 6VD1 SOHC V6
3.2 L 6VD1 DOHC V6
3.5 L 6VE1 DOHC V6
3.0 L 4JX1 TD I4
3.1 L 4JG2 TD I4
x1 or G2?

floods, wot cranking cuts fuel and starts any flooded engine,
it's overheating that wins the First order failures rule sets.
nothing else matters. cure that first.! find cause! first.

sounds (im deaf there,lol) that smoke is out tail pipe end and dissipates fast and is not smoke but steam, , oil smoke smells like burning oil and lingers. steam smells sweet like burning Antifreeze.
AF steam is a blown head gasket or far worse.
do a compression test first to see if it's even worth fixing????
most are NOT. (unless free labor, sure)

first learn steam from smoke
serious , watch moms tea pot. see that steam goes away fast.and very uniquely , now watch burning oil.
remove dip stick, drop the drip of oil on hot exhaust manifold.
smell that, that is oil burning, and lingers.
this will last you a life time of blown engines..... just one look and bingo. (my instructor in 1965 did in front of class)

got oil in the AF/ CARBON chunks in same.
water in oil, ? pan, engine . milky oil.
rad leak down test fail? can be lots of reasons even a cracked block.or head. not just gaskets.

Honda motors are 4 stroke motors so I would be checking if you have put 2 stroke mix in the fuel tank and that is the oil smoke problem. IF you are running straight petrol then there is a problem with the oil ring unless you have over filled the sump.

The thick white smoke is either burnt oil or steam you can easily identify the smell of burnt oil not really sure why you thought it would be a good idea to put a 2 stroke mixed fuel in but more than likely that alone fouled your spark plugs. But if the problem preceded the fuel blunder then your either have a bad intake/head gasket, leaking valve seats, or bad main engine seal. Replace the spark plugs and check cylinder compression. Change your engine oil and check to see if it contains water/coolant also watch for coolant or oil consumption

You don't mention what that smell is reminiscent of?

You don't mention the colour of the "smoke" and you didn't say whether the engine is petrol or diesel?

You don't mention whether the road behaviour/performance is normal?

White smoke is almost always steam or in the case of a diesel it could be an unburned fuel mist, grey/black is excess fuel and blue or grey/blue is burning oil.

Some steam is fairly normal until the engine and exhaust system is hot but excessive amounts could be one symptom of head gasket trouble. If the engine is drinking coolant and sending it through the exhaust as steam it will sometimes smell spicy.

Burning oil smells a bit like burned eggs in the frying pan.

If the car hasn't ultra-low sulphur oil and fuel the catalytic converter will convert sulphur traces into hydrogen sulphide - the bad egg gas...

Steam is not smoke. Smoke would be from oil burning, the steam would be overheated coolant which is 50% H2O. Oil making white smoke, more than a little would have a smell that irritates the eyes and nose
while the steam from overheated coolant will smell sweet. The mixing of coolant and oil will be apparent on the oil fill cap when major damage has occurred and looks like coffee with cream.

If it doesn't smell like sweet then you most likely got a bad tank of gas. Just to be safe keep an eye on your engine temp. and coolant levels.

The key is the color and smell of the smoke.

IF coolant, the smoke is REALLY white and usually lots, and this smoke has a sweet smell. A pressure test may show some loss, and as well, often you get a little misfire that goes away.

If Oil, the color is white, but with a lot of blue, or darker...

Most of the time, after the converter warms up, it eats and converts both types of issues...

Steam, can be normal. Remember that for every gallon of fuel you burn, you actually generate 1 gallon of water. Typically evaporates or exits as steam, and is barely perceptable.