In the chastening campaign, Australia record four comprehensive wins -- including two innings victories and a 10-wicket triumph.
Stokes missed the entire series in Australia after being banned from international duties while police investigate his alleged role in a fight outside a nightclub in Bristol three months ago.
He kept his hand in by playing for Canterbury, his New Zealand birth province, for a month, but has since returned home to be with his wife and young family.
"Should the ECB Board receive formal confirmation that Stokes has either been charged or that he will face no charges, they would convene within 48 hours to make a decision on his availability for the team at that stage," they said.
Livingstone was rewarded for his form with Lancashire, with National Selector James Whitaker saying they had been watching him for some time.
"Liam has been a player that we have been impressed with for quite some time, having performed well in the county system with Lancashire and over the past couple of years with the England Lions," he said.
"He is a very talented and tough cricketer who has the ideal qualities and character to be successful in the Test arena."
Selectors also recalled Durham seamer Wood, who is back in the Test squad for the first time since last year.
"After a frustrating period with injuries, Mark is now back to full fitness and is looking forward to being part of our Test plans," said Whitaker.
"He will play a significant part in our forthcoming ODI tour of Australia and we will be paying close attention to his efforts over the next few weeks."
England play five one-dayers against Australia, starting in Melbourne on Sunday.
From the Ashes Test squad, Yorkshire batsman Ballance, Nottinghamshire seamer Ball and Surrey all-rounder Curran all miss out and will return to county cricket.
"They are talented players and I am sure their time will come again," said Whitaker.
England - Joe Root (capt), Moeen Ali, James Anderson, Jonny Bairstow, Stuart Broad, Alaister Cook, Mason Crane, Ben Foakes, Liam Livingstone, Dawid Malan, Craig Overton, Ben Stokes, Mark Stoneman, James Vince, Chris Woakes, Mark Wood.
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