Is there any realistic, cheap way to change a car into a pedal-driven vehicle you can ride yourself?
(I'm not quite sure if this is the right category to ask, but I couldn't find a better one.)
Since that's way too short for an answer, lets look at some maths.
An average car might weigh
Lets say you start with one of the lighter cars, a Daihatsu Charade gen3 from 1988-1991. This car weighs 740 to 760 kilos, or as much as 50 15 kilo bikes, or 110 UCI legal race bikes at 6.8 kilos. Source: https://en.wikipedia.org/wiki/Daihatsu_Charade
What parts can you remove and still call it a "car"
So a total of 26% plus a lot of unknowns.
Flipping it about - how much do you need to keep? So 24% of your car is "structure" which will cover chassis. The external panels add 5%. Wheels and tyres are needed to roll, brakes to stop, that's 10%+3% Suspension can probably be lightened because of the weight drop but you'll still need half of it at 5.5%. Interior of 10% could be reduced by half to 5%. For a total of just over 50%
Lets assume you can HALVE the weight of your lightweight car by removing non-essentials. That leaves 375 kilos of dead weight that you still have to move around.
And that's simply ignoring the weight of your pedal propulsion system still to add.
Lets go one step further and assume you did all this, and end up with a 375 kilogram bike shaped like a car. Also assume you have managed to keep the 4 seats.
Using http://bikecalculator.com/ we can guessstimate your speeds.
1 rider of 75 kilos, putting down 150 watts get about 9.4 km/h on the flat with zero wind.
Same rider gets 1.9 km/h if the gradient picks up to 5%
If that single rider were on a 10 kilo road bike, they'd be getting 10.8 km/h up the same 5% grade
...OK but its a 4 seater...
4 riders of 75 kilos each doing 150 watts would get about 22.8 km/h on the flat.
Same 4 riders on the 5% hill get 5 km/h
Taking it to the extreme, 40 riders in your car each weighing 75 kilos and adding 150 Watts, would climb the same grade at 10.0 km/h, not as fast as one of their number on a 10 kilo road bike.
Turns out you need 265 cyclists in your car to match the single road bike on this simple climb. Collectively that's 20 tonnes of cyclists inside your 375 kilo stripped out car.
Why are cars so heavy? Because the kinetic energy required to drive at open road speeds needs a chassis of a certain minimum strength. And if you want that chassis to last more than one trip it has to be overbuilt which means adding strength through thickness.
Car seats are very heavy, a racing car seat might be 3 kilograms and a conventional single seat anything from 20 to 70 kilograms depending on motors and armrests. They have to hold and protect the occupant in a collision with hundreds of km/h difference in speed. Your average 500 gram bike saddle doesn't have those requirements.
There are people who have gone the other way, and wrapped an enclosure around a bike rather than stripping a car down to find the bike inside.
The PodRide weighs 70 kilograms, and is a cloth and tube frame around a recumbent-style frame.
Legally its an electric bike, at least in Sweden.
You did not specify the scope of your question, i.e. does something that looks like a car count? If yes it is possible.
You can do it by buying a four wheeled bicycle and building a lighweight (wooden? plastic pipes + tape? don't forget paint!) framework around it in the shape of any car you want.