Fa'alogo, the 32-year-old former New Zealand Test back-row forward who joined the club from South Sydney three years ago, was not offered a new contract and played his last game for the Giants in Sunday's 46-10 play-off defeat at Hull which ended their season.
Huddersfield also declined to offer a new deal to former St Helens hooker Moore, 24, who joined the club for a second spell in mid-season after being sacked by Widnes.
Former Hull, Crusaders and Wakefield half-back or hooker Lee, 24, rejected the Giants' contract offer and is set to join London Broncos.
Huddersfield will be able to command a transfer fee for 21-year-old prop forward Walker after he rejected their terms.
He played in four of the club's opening five Super League fixtures of the season before going on a dual registration to Swinton.
"The club would like to thank all departing players for their contribution to the claret and gold and wish them well for the future," the club said in a statement.
Huddersfield have also parted company with Kevin Brown and Lee Gilmour and so far have signed Widnes forward Anthony Mullally and prop Akuma Ta'ai from New Zealand Warriors.