All three have agreed deals until the end of the season.
Cobblers boss Gary Johnson signed goalkeeper Collis, 29, and 20-year-old right-back Ofori-Twumasi when he was Posh boss in the summer.
Reckord, 19 on Wednesday, has yet to make a senior appearance for Wolves but has represented England Under-17s.
"Jamie is primarily a left-back and he was very close to joining Swansea on deadline day in January," Johnson told the club website.
"If he does well there is a possibility that we could take him on a season-long loan next year."
Collis played under Johnson at Yeovil and Bristol City but has yet to feature for Posh since joining in August.
"Steve is a person I know well," added the Cobblers boss.
"He is someone who has been with me before. He plays well, he trains well, he has a great attitude and is a player I can trust. I have been impressed with Chris Dunn, but Chris needs competition and needs to battle with Steve for a place in the team."
Ofori-Twumasi, who was released by Chelsea in the summer, has played 16 times in his debut season at London Road.
"Nana can play as a right-back or centre-half and he can also cover in midfield," said Johnson.
"He has got power and pace and we have brought him in with a view to making the move permanent if everything goes well."
Source: BBC Sport
Source: BBC Sport