As Sean Clifford's blindside blocker, Walker earned third-team All-Big Ten honors in both 2020 and 2021.
Hazel has been a key member of James Franklin's staff since the head coach arrived at Vanderbilt.
Luketa announced his decision shortly after Penn State's Outback Bowl loss to Arkansas.
Arkansas scored 17 unanswered points in the second half to cruise past Penn State.
Avery plays both defensive end and tight end at Our Lady of Good Counsel High School.
In a statement, Penn State said its leadership felt current COVID-19 conditions don't require a switch to online learning yet.