Speaker wire requirements in the car would be the same as those at home for amplifiers of similar output powers in both cases.
Or slightly higher, as it is not uncommon to see the likes of 2-3 ohm subs.
On a speaker wire, impedance levels are super low - we are talking hundreds of milliohms of amplifier output impedance or less - and speakers are extremely insensitive and floating loads to boot. Even if twin lead is not quite the ideal cable topology it doesn't matter, at least at audio frequencies, and the most interesting aspect becomes ohmic resistance.
The best kind of cable for line-level
unbalanced connections is coax. If you are a cheapskate who needs some particularly lengthy ones that are about as good a cable as you're going to get, buy some composite video cables using RG-59. That's what I bought when I needed 10 meters for a tuner two decades ago. The most important single parameter may be shield coverage and resistance, although capacitance also matters (particularly on long runs or for these pesky MM phono cartridges).
The best cable for line-level
balanced connections is shielded twisted pair. Hence why you can make perfectly serviceable ones using ordinary network cable as long as it is typical FTP or STP (not so much UTP). It is obviously not going to stand up to the rigors of stage use but if you need to get up to 4 channels of audio from point A to point B in a stationary application it's fine. Good microphone cable also needs to be flexible, robust, and low in microphonics both mechanically and electrically (bad cable stock can generate all sorts of unwanted rustling as soon as phantom power is turned on), and for particularly tough environments and/or long runs you can buy starquad which improves symmetry for better interference rejection.
Headphone cable is a similar kind of situation as speaker cable, except it needs to be super lightweight and still reasonably durable and non-microphonic. As long as both drivers are wired up individually all the way to the plug, resistance is kind of secondary thankfully. It is not uncommon to find kevlar fiber reinforcement for increased strength (Sennheiser found out the hard way that just copper just doesn't last back in the day, which is why they used steel wire for a while in the '80s which was a bit non-ideal due to microphonics).