Lock Stooke, 22, joins from Premiership rivals Gloucester having made 70 appearances for the Cherry and Whites.
Back row Preece, 26, arrives from Coventry RFC, while 27-year-old New Zealander Halse has been playing in Italy and can play at fly-half, inside-centre and at full-back.
All are eligible to make their debuts on Saturday against Northampton Saints.
It was confirmed last month that Stooke would join Bath following the completion of his current deal.
"We are currently battling with an extensive injury list and quite a number of those are long term," said London Irish's head of operations Glenn Delaney. "The three players will be solid additions to our squad as we continue in this block of Premiership fixtures."
London Irish, currently bottom of the Premiership, are already without second rows George Skivington, Eoin Sheriff and Nic Rouse because of long-term injuries.
London Irish have signed forwards Tom Preece and Elliott Stooke and back Tom Halse until the end of the season.