You could do what they did on the original film, which was to buy a commercially made RC car and then fabricate a body for it. They probably used the lid off a plastic trash can painted black and with those spikey things added. I'd probably use some thin plywood and do a good finishing job on it if I couldn't find a suitable trash can. A $20 toy grade on road type car would do the trick. As for the sounds, it's simple enough to pair your phone with a Bluetooth speaker and have it tweet and chirp to your heart's content. If you want to control those things with your RC transmitter, that would require setting up an Arduino or similar product to play sound files in response to your commands.