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."
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