Q:

For cars, what verb has to be used? Stehen oder liegen?

I'm highly confused with what verb should be used with automobiles. If I consider the car "stands" then stehen but it's in a horizontal position, so I suppose it could be liegen as well.

A:

A car has wheels. If it is not moving, and all wheels (but nothing else) are touching the ground, then you say:

Das Auto steht auf der Straße.
  The car stands on the street.  

After an accident the car can end sideways or upside down. So non or at least not all of its wheel touch the ground, but other parts (door, roof) touch the ground. In this case you can say:

Das Auto liegt auf der Seite.
  The car is lying on it's side.  
Das Auto liegt am Dach.
  The car is lying on it's roof.  

But there is another term, that is similar to »liegen« (to lie). This is »liegen bleiben« (literal: to stay lying). For vehicles this means that you car's engine is broken, or you ran out of gas, or you lost a wheel, and therefore you can't drive any longer with it. To be precise: It means, that for technical reasons, but without having an accident, you suddenly can't drive the car any longer.

Mein Wagen ist oben im Wald liegen geblieben, und ich musste den Weg hierher zu Fuß gehen. Er steht jetzt auf einem Forstweg.
  My car broke down up there in the woods, and from there I had to walk all the way to come here. It stands now on a forest road.    

A:

Well what comes in my mind at first are these option:
abstellen, parken und stehen/stehen lassen.
So it depends on the context: 
If you want to express that your car is (standing) in a location as for example you say my car is parked in X-Street:

Mein Auto steht in der Goethestraße.  
Mein Auto steht vor der Goethestraße 9.  
Mein Auto ist in der Goethestraße geparkt/abgestellt.

But if you want to express that you left your car (standing) somewhere then it's primary the other options that would fit. 
Here some examples:

Ich habe mein Auto neben der Metzgerei abgestellt!  
Ich habe mein Auto am Straßenrand geparkt.  
Ich habe mein Auto vor der Haustür stehen lassen.  

Special case mentioned in the helpful comments of Matthias and PattaFeuFeu and also in Huberts great answer:
Well as my first impression about the Question was the normal state a working car that stands or is parked somewhere, i didn't mention the options that may allow using the verb "liegen" or "liegen bleiben".
So after a car breakdown one could say:

Ich bin mit meinem Auto liegen geblieben
Mein Auto ist nach einem Motorschaden liegen geblieben

But in case of an accident when the car doesn't stand anymore on its wheels one also could use liegen:

Nach dem Zusammenprall lag mein Auto auf der Seite im Straßengraben.

An other special case are toy-cars who may lay scattered in the room as Stephie mentioned in her helpful comment:

Die Spielzeugautos (Autos) meines Sohnes liegen überall im Wohnzimmer herum.

