Both players join the League Two side until the end of the season.
Nelson, 19, is yet to make a senior appearance for the Black Cats but has played two under-21 games in the EFL Trophy this season.
Northern Ireland Under-21 international Rooney, 20, has played just three times this season but scored twice against the Pools on his Argyle debut in May.
He was on the bench for Plymouth's 2-1 defeat at Yeovil on Tuesday night, with the club saying his move to the north-east went through just 17 seconds before the transfer window shut.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.

Karoo national park authorities had originally considered putting Sylvester down but will now rehouse the animal away from male competition.
The lion's plight was highlighted in a Twitter campaign in South Africa.
Sylvester will now join two young female lions in Addo Elephant National Park in the Eastern Cape province.
Sylvester escaped at the end of March by crawling under an electric fence after heavy rain dislodged earth, a park spokesperson said at the time.
It is thought three-year-old Sylvester was running away from threatening older males.
The move will establish him as the dominant male, said Fundisile Mketeni, CEO of South Africa National Parks.
"There is always a risk that this lion may break out again but this will be mitigated to a large extent by reducing any potential conflict with other males," Mr Mketeni added.
Last June, Sylvester went on a three-week sheep-killing spree, wandering 300km (180 miles) before he was found taking a nap by rangers and airlifted from the Nuweveld Mountains.
When he was found he was fitted with a tracking collar.
The second time he escaped, rescuers followed the signal from his collar to find him high up in the mountains in Western Cape again.
He was tranquilised and airlifted by helicopter, an operation the park authorities captured on video.
He had been away for four days.

The 45-year-old led the Cumbrian side to seventh in the National League this season, seven points off the play-offs.
Pools defender Matthew Bates had been in caretaker charge of the side after Dave Jones left in April.
Barrow owner Paul Casson has stated Cox has a sizeable buy-out clause.
Hartlepool's relegation on the final day of the season meant they dropped out of the Football League for the first time in 96 years.
Hartlepool have signed strikers Andrew Nelson and Louis Rooney on loan from Sunderland and Plymouth respectively.
[NEXT_CONCEPT]
A South African lion called Sylvester who twice fled a national park will be rehoused rather than put down, and encouraged to become an alpha male.
[NEXT_CONCEPT]
Relegated League Two side Hartlepool United have been given permission to speak to Barrow manager Paul Cox about their vacant managerial position, reports BBC Radio Cumbria.