Former Plymouth keeper McCormick, 29, has been playing at non-league Truro City following his release from prison last June after serving a four-year sentence for causing death by dangerous driving.
"We are very mindful of the past and the situation," boss Chris Wilder told the club's official website. "Luke is very contrite and sorry about what happened. He was sentenced and went to prison and during that time had the opportunity to reflect on what he had done.
"It is hard to separate the two but purely from a football perspective he is an experienced goalkeeper who has played most of his games in League One and the Championship.
"We have a situation here where our number one goalkeeper is out for the foreseeable future with a shoulder injury and we could lose Max Crocombe to international duty next month. We are offering Luke a chance to play again.
"I have spoken to Luke at length and he knows it will not be easy for him but he is very humble and wants to try and make the most of the opportunity."
Striker Richards, 32, has been on loan at the Kassam Stadium from League Two rivals Burton and makes his stay permanent.
"I'm pleased" he said. "I have really enjoyed my time at Oxford.
"The players and fans have made me feel very welcome. It is a club that is moving in the right direction and I hope I can play a part in a successful second half of the season."
Elsewhere, 19-year-old striker Tyrone Marsh has joined Staines Town on loan until the end of the season.