Laycock battled injury through his seven years at the Bombers, and played 58 matches for the club, with the last back in round 20 2008.
Also gone is rookie John Williams, who played one game for the club in round 22 of 2008 against St Kilda.
Richardson applied for the senior coaching job at the Bombers after Matthew Knights was sacked, and has now moved to the Blues in the wake of club legend James Hird being appointed.
Football manager Paul Hamilton said Richardson left with the best wishes of everyone at the club.
"Alan has been offered a very senior coaching role at Carlton and, considering one of our big philosophies at Essendon is about developing people, we were never going to stand in his way," Hamilton told the club's official website.
"He has made a strong contribution over his two years at the club and is highly respected by everyone at the club."
Former skipper O'Donnell is also moving on, after coming to the Bombers for the 2005 season.
"Gary is looking to move onto the next stage of his career after holding assistant coaching roles at Essendon under Kevin Sheedy and then Matthew Knights," Hamilton said.
"Gary has made an enormous contribution to the club in a wide range of areas and he is someone that we have the upmost respect for.
"He has been a great player, captain and assistant coach for the Essendon Football Club and is someone that we hold in the highest regard."
