Hall, who made 82 appearances for the U's between 2010 and 2012, spent last season with Shrewsbury and joins United on a six-month loan.
Former Rotherham and Cambridge left-back Newey joins on a one-year deal after leaving Scunthorpe.
"They are both very experienced solid players and they add a bit of depth," manager Chris Wilder told the club's official website.
"Tom adds balance on the left side of defence and is a very good organiser as well as a good player. Asa showed us towards the end of his first spell here what a good player he can be at this level."
Oxford have already signed David Hunt, Jon Meades, Danny Rose, Josh Shama and Dave Kitson ahead of their first pre-season game at Ardley on Saturday.