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.
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Hartlepool have signed strikers Andrew Nelson and Louis Rooney on loan from Sunderland and Plymouth respectively.