The killings took place on Thursday and yesterday in Dikwa, Kala-Balge towns and near Dalwa village in the state, the bastion of the Islamist sect, they said.
In Dikwa, one of the ancient towns in Borno State, residents said that insurgents stormed a college in the early hours of Thursday, killed six teachers and two security guards and abducted an unspecified number of women, the residents said.
A witness, Modu Kakarimi, who fled Dikwa to Maiduguri, the state capital, said he and some others ran away to safety when they heard sound of gunshots.
Bono state Senator Ahmed Zanna confirmed the Dikwa killing to journalists but he said he could not provide full details.
"There was a siege on one of the schools in the town just after midnight... They also razed the school library and escaped into the night through the bushes," he said.
A group of insurgents also attacked Kala-Balge town, killing three people and setting many houses ablaze, some local officials said on condition of anonymity.
Ali, who passed through Dalwa on his way to Maiduguri said the insurgents stormed the highway in broad daylight.
There was no immediate confirmation of the attacks by security agencies but a top security officer, who demanded anonymity, confirmed them.
"There were various attacks in the state...It is sad," he said.
The military is launching a major offensive in the region to crush Boko Haram's uprising, which the insurgents say is aimed at creating a strict Islamic state in northern Nigeria.