What are they?
The developers made Mafia with some extra models (these models are stored in a single file named with the extension .4ds) in the game. The only way of using these secret cars is to rename one of the secret car models to the name of a car model that is already in the game.

Extracting
First of all you need to get a copy of MafiaDataXtractor available from this site in Downloads/Tools. This patches the game so that it can read information stored in folders. All of Mafia?s files are stored in .dta archives with the game patched it will look if there?s any files it can use in the folders, If not it will just use the files in the .dta archives.

Launch MafiaDataXtractor and extract models.dta. This will extract the models to your mafia folder under the folder models. Open your newly created models folder (there will be only a few files you'll use in here. The rest you can just ignore/delete).

Renaming
The renaming works like this:
e.g. fordtTud00.4ds is the Bolt Ace Tudor and bus.4ds is the secret bus. Delete or rename fortTud00.4ds so Mafia ignores this file, and rename bus.4ds to fordtTud0.4ds. Mafia will now open the bus model if you select the Bolt Ace Tudor in Freeride or Freeride Extreme.

Models and physics
These are the secret car models:
bus00.4ds - Big cream bus
bull00.4ds - Bulldozer
Salina.4ds - Tram (can't be used; only be seen in Carcyclopedia)
toyota.4ds - Toyota Concept Car
bigfoot.4ds - American monster truck
bigfoot00.4ds ? Brown Monster truck
traktor.4ds - Tractor
brouk00.4ds ? Customized Beatle
xedos00.4ds - A Rover

You could use these models to replace them with:
cad_road00.4ds - Lassiter Roadster, top speed 100 mph with very good acceleration.
cad_phaeton00.4ds - Lassiter Phaeton, top speed 88mph.
airflTUD00.4ds - Ulver Airstream Tudor, engine sound is more like modern cars with average speed/acceleration.
airflFor00.4ds - Ulver Airstream Fordor, same as above but the four door model

Since you have only change the model or the shell of the car, the properties i.e. acceleration, cornering, physics realism, top speed will all match that of the car that Mafia thinks it is using. So for faster cars like the Toyota or Rover, it is best to use a car that has closer matching properties.

Uninstalling the secret cars
If you want everything back how it was, so all cars are how they were, just delete the models folder and mafia will use the files in the .dta archive instead.