Both players made their debuts against Shrewsbury Town in the second round of the League Cup last Tuesday which United won 4-3 on penalties after a 0-0 draw.
20 year old Mulligan joins Port Vale, who could have joined others, but Neil Warnock chose the League One side.
Vale boss Martin Foyle has brought in the former Wolves trainee as cover while Lee Matthews is out injured; "It gives us a striker while we wait for Lee Matthews to get fit.
"There were three other clubs chasing him, but I would like to say a big thanks to Neil Warnock, who has helped me out at a difficult time.
"The lad comes with a good pedigree and hopefully we can use him and throw him up front and he can have a say in our attack." Foyle told port-vale.co.uk
Meanwhile Irishman Stephen Quinn has joined troublesome MK Dons whose win this Saturday at Blackpool could lift them off bottom of League One.
Both young players have joined their respective clubs on a months loan with them returning to Bramall Lane once their spell is over. Quinn and Mulliganm are also expected to make there debuts this weekend.