Is there a way to turn off car damage?

You could create a mod and build a lua file that modifies the HitPoint() value for each .con file you have in the game.
Create a .lua file called HandleCars.lua & write in a function to modify the files.

local path = "/GameData/"..GetPath()
local file = ReadFile(path)
if file ~= ReadFile("/GameData/scripts/cars/huskA.con") then
file = file.."\n\n".."SetHitPoints(51);\n"
Output(file)
end

Thankfully to DT we've got some really useful custom functions for lua working with the game.
I remember having my code typed after some of DT's mods so all credit for the code to them. Hope this helps!

Alternatively, use the game's vehicle invincibility cheat code.