Belgium international Lukaku, 20, and Barry, 32, join on season-long loans.
Everton have stated that McCarthy, 22, has signed for £13m, but Wigan say the fee is in the region of £15m.
The Toffees have also confirmed the departure of Marouane Fellaini to Manchester United for £27.5m and Victor Anichebe to West Brom.
Lukaku, who signed for Chelsea from Anderlecht in August 2011 for a reported £20m, spent last season on loan at West Brom, where he scored 17 Premier League goals.
He has appeared as a substitute twice for Chelsea in the Premier League this season and missed the decisive penalty in the Blues' Super Cup defeat by Bayern Munich.
The Baggies were hoping to bring Lukaku back to The Hawthorns but Everton beat them to his signature to offset the departure of Anichebe to West Brom.
McCarthy, who has played 16 times for the Republic of Ireland and was part of Wigan's FA Cup-winning side last season, was brought in to fill the void left by Fellaini's departure.
Everton have not revealed the length of his contract, describing it as a "long-term deal", while his former club Hamilton Academical have also received a substantial sell-on fee from Wigan.
England international Barry signs after making 132 Premier League appearances for Manchester City.
The former Aston Villa man, who helped City to FA Cup and Premier League successes, is in the last year of a five-year deal with the Manchester side.

Gareth McAllister, 18, is also accused of inflicting wounds on a 74-year-old man during a triple stabbing in Glengormley, County Antrim.
All three alleged victims are members of the same family.
Mr McAllister, of Rogan Manor in Newtownabbey, was arrested at a nearby petrol station on Wednesday night.
A man aged 20 had suffered a slash wound to his forehead in an alleged attack at the house on the Antrim Road.
His 51-year-old father and his grandfather also sustained cuts as further violence broke out at the nearby garage, according to police.
Mr McAllister appeared before Belfast Magistrates' Court on a total of 10 counts.
He is charged with the attempted murders of Jonathan and John Green, and assault occasioning actual bodily harm to Derek Green.
The other alleged offences include: possessing a bread knife in public; four assaults on police representatives; a separate assault on John Green last Saturday; and criminal damage to his front door.
Mr McAllister spoke only to confirm he understood the charges against him.
Although no further details were disclosed, a detective constable said he could connect the accused to the alleged offences.
A defence lawyer said he was not applying for bail "at this time".
A judge remanded Mr McAllister in custody to appear again by video-link next Thursday.
Everton have signed Chelsea striker Romelu Lukaku, Wigan midfielder James McCarthy and Manchester City's England international midfielder Gareth Barry.
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A teenager has been remanded in custody charged with the attempted murder of a father and son in a knife attack on the outskirts of north Belfast.