The arrested four suspects, all male, are Kelechi Nwali, Onyebuchi Chita, Aloke Obinna and Ifeanyi Nwokpuku.
In the video, a man could also be heard speaking Hausa, confirming that the deceased was in his shop before he was hit by the stray bullet.
Mr Odoh was ambushed while returning to Abakaliki after the party’s campaign outing.
Mr Oyeyemi said detectives arrested the suspect on Sunday in Akinseku Village, Abeokuta, where he had gone to hide after committing the alleged crime.
The 38-year-old suspect also murdered a witness who saw him killing his mother-in-law.
The illegal Excellence College of Health Sciences in Maikunkele, Bosso LGA, had about 20 teachers.
Some of the suspects also helped negotiate and deliver ransoms from families to the kidnappers for a commission.
The command said the three-man gang specialised in robbing people of their vehicles and other valuables at gunpoint.