Is this possible on a 24-hour VOA?

Shenzhen now has the 24h twov, and you can apply for it after arrival at the immigration counter of the airport.

perfect. thank you very much

Did you recently go do a layover in Shenzhen. In IATA it says that the TWOV does not apply to Shenzhen? I am confused. I need to do a layover there and would require a visa if TWOV is not available.

Shenzhen does now have 24 hours transit without visa, but it is not available for transits to Hong Kong or Macao.

Ok which means I can freely drive to Hong Kong because I am traveling to Vietnam the same day, right?
HK alone wouldn't work. Going via HK to another non-Chinese destination will?!

Last question (to make it even more confusing) Can I do a one-night layover in HK? Do they have the 72-hour direct transit?

Hong Kong has totally separate immigration rules from mainland China, and EU citizens don't require a visa for stays of up to 90 days (except UK citizens, 180 days). But you cannot transit from Shenzhen to Hong Kong without getting a Chinese visa in advance.