Oldham had not won in the league since 18 October under Robinson, 42, and the Latics are three points from safety.
After working as Northern Ireland's assistant at Euro 2016, his first managerial role lasted six months.
Sheridan left Oldham in the summer for Notts County but he was sacked by the League Two club on 2 January.
The 52-year-old former Latics midfielder has taken over almost a year to the day since doing so in similar circumstances last season, when the club were relegation zone, but Sheridan guided them to 17th place and safety.
"This is obviously a difficult decision," chairman Simon Corney told the club website. "Stephen is a talented coach who we believed could make the transition into a successful manager.
"Unfortunately things have not worked out for him or the club and we felt that a change needed to be made.
"John is obviously someone we know well and we hope he can have an immediate effect on our current situation."
Robinson had to work under financial pressures at Oldham as he started pre-season with seven contracted players and the club had been under a transfer embargo since November, but this is expected to be lifted.
The Latics struggled for results during his tenure, have been in the bottom four since 24 September and are the lowest scorers in the English Football League with 12 goals in 24 games.
Sheridan's first game in charge is Saturday's match at home against Gillingham.
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