I have a question about the correct preposition to use. Suppose context is a driving car:

1. The car went into/onto a curve.
2. The car went into/onto a path.
3. The car went into/onto a road.

Should it be "into" or "onto"?

Depends a bit on context. As polynom points out usually you want to use drove with a car and for most cases you will want onto a path/road.

With curve it's actually different since the curve isn't something you can usually reasonably drive "onto". Unlike a path or a road it's usually not "long" enough to allow driving onto.

The car drove through the curve.

Works ok, if the drive just passed the the curve. If the car is currently in process of transitioning through the curve you would actually use "into" since the curve is a bounded area in which the car currently is.

The car drove into the curve at some speed.

One place where you could use onto with a curve might be mathematics. There the curve might be a curve in space and you could have a car drive onto it.

Note also that you can also use:

The car turned into a sidestreet.

They all are surface so I think 'onto' fits better. Also, the word 'onto' has 'to' in it which means direction, the movement. In all those sentences, the car was somewhere else and then it moved, directed toward a curve/path/road. So, my vote is for 'onto'.

INTO a curve; ONTO a path or road. Just another of our English idiosyncracies that make no sense. You're really not talking about the pavement when you're talking about the curve, it's more of the direction, not the pavement.