Ex-Bolton and Watford man Sordell joins on an initial contract until June.
Striker Beavon, 32, moves on an 18-month deal, while midfielder Reilly, 23, is on loan until the end of April.
Sordell, 25, who has netted seven times in 26 games for Coventry, leaves six months into a year-long deal.
Burton will be the forward's eighth club in less than eight years, having started his senior career with Watford in 2009 before moving to Bolton then Burnley, Colchester and Coventry.
Sordell, who featured for Great Britain in the London 2012 Olympic Games, also previously had loan spells at Tranmere and Charlton.
Beavon, who helped Burton win back-to-back promotions to reach the Championship this season, leaves the Brewers after almost three years with the club.
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Coventry City leading scorer Marvin Sordell has joined Championship club Burton, while Stuart Beavon and Callum Reilly have moved the other way to sign for the Sky Blues.