I assume you're talking about the sounds you hear right after you shut it off.
Normally you can hear various ticking sounds from under the hood and even under the mid section of the vehicle for a few minutes after you shut it off. These are the various components cooling off. Many materials will make this sound as their temperature is changing. The noisiest part of a vehicle when sitting hot is the exhaust system.
This, by the way, is the same phenomenon that you may hear in your house after you have just run hot water then turned it off. As the pipes cool they can tick or sometimes bang.
check oil level. go to engine shop.
To muffle the sounds of the engine /exhaust coming out take it off and see how it sounds!
because the engine is still processing the oil for about 20 seconds after you turn the car off
A cooling engine always makes little tics and clicks, especially if it's really hot and the weather is cool.
This is a problem with fuel delivery. Sounds like you need to change the fuel filter. If the engine stumbles even at higher revs, one of the cylinders is failing to ignite.
The frist thing I would check would be the engine mounts.
Because the engine provides the power to operate the drivetrain, which is what makes the car move in the first place. Turn the engine off, and there is no more power going to the drivetrain - the remaining movement of the car until it stops is simply inertia.
probabaly a knock sensor going off
sounds like you need a valve job. how many miles on this car?
It sounds like your dizzy cap isn't lined right which causes the engine to stay running after the ignition has been switched off. i had the same problem with my fiesta
If the car has a lot of miles on it, it's probably the motor mounts.
It Will usually have an air pocket in the cooling system. But it may just be the Air Conditioning equalising after you shut the car off. Start by filling the cooling system