Neither Olayinka, 19, nor Morton, 20, have made a first-team appearance for their parent clubs.
But they have both featured for the academy sides in the Leasing.com Trophy for their respective teams.
Morton scored five goals in 14 games for Braintree in the National League last season while on loan.
"James is a dynamic midfielder who we saw play well against us earlier in the season," Cobblers manager Keith Curle told the club website.
"We have tracked him closely and seen him play in a number of under-23 games and he has always impressed us.
He added: "Callum is a striker who likes to play in behind defences. He can handle himself physically, he knows where the goal is and he can be a threat.
"He has a great work ethic, he will chase everything and he is a real nuisance to play against. He is desperate to make an impact, he has that hunger about him and he has got good ability."