Garside, 21, can play in the back-row or at centre, and has scored 15 tries in 46 games for York since arriving from Gateshead in 2011.
Eagles coach Mark Aston said: “I’m delighted to have to signed Matt for 2013. He’s big and strong and will add to the squad.”
Club captain Howieson has agreed to a new one-year deal while Laulu-Togagae, who broke the club record for most tries in a season this year, will stay until the end of 2014.
“Jack’s has been with us for around 10 to 12 years and it’s great for the club captain to be sticking with us.”
Samoan international Laulu-Togagae, 27, joined the Eagles from Brisbane club Souths Logan Magpies ahead of the 2011 season.