The expected departure of Marouane Fellaini to Manchester United enabled Martinez to match Wigan chairman Dave Whelan's B£13million valuation of McCarthy, while Lukaku and Barry arrived on one-year loan deals.
Fellaini completed his B£27.5million move to Manchester United after a long period of speculation which included the Belgian driving to Everton's training ground to hand in a deadline-day transfer request.
Martinez responded by landing McCarthy, whom he had first brought to the Latics in a B£1.2million deal from Scottish club Hamilton, with the player quickly establishing himself at the DW Stadium.
Lukaku scored 17 goals in 35 appearances on loan with West Brom last season and it appeared at one point that the 20-year-old Belgian was all set to return to The Hawthorns.
But Everton pounced with a more attractive offer to the player, who had returned to Stamford Bridge in the summer but found his first-team chances similarly restricted under new boss Jose Mourinho.
Meanwhile Martinez landed an experienced midfielder in 32-year-old Barry, who like Lukaku was keen to move in order to secure more regular first-team football.
The deal taking 25-year-old Anichebe to West Brom could eventually rise as high as B£6million.
A graduate of the club's academy, Anichebe made 168 appearances for the Blues and scored 33 goals.