Vidanga means something that has not been chiseled out.
These 7 temples are called Saptha Vidanga Sthalams. The King, on return to earth, installed all the 7 moorthams at various places as Thyagarajars, keeping the original one at Thiruvarur. Indhra was so happy with the devotion of Muchukunda Chakravarthi and gifted all the 7 moothams to him. Muchukunda, a great devotee of Lord Shiva, picked the correct one with the help of Lord Himself. So Indhra played a trick by asking Visvakarma to make six more similar moorthams and offered all of them to the King asking to choose any one. Muchukunda Chakravarthi was not accepting any other gift. As a thanks giving, Indhra offered whatever the King wanted but Indhra was shocked when the King, a staunch Shiva devotee, asked for the Somaskantha moortham Indhra was fondly worshipping which he got from Lord Vishnu Himself.
Once Indhra sought help from Muchukunda Chakravarthi, a great valorous monkey faced king to fight against demons and they won it also. Later this was gifted to Indhra by Mahavishnu. Mahavishnu kept the Somaskanda moortham in His chest and it danced gently to the breath of Mahavishnu’s breath which is called the Ajaba Dance of Sri Thyagarajar at Thiruvarur. Then Parvathi Devi got satisfied and gave a blessing that their son would be burnt by Shiva’s third eye but will get into life after. So Mahavishnu made a Somaskanda moortham (Murugar in between Shiva and Parvathi) and worshipped. So Parvathi Devi gave a curse that though a son (Manmathan) will be born to them as per the granted wish, he will not have longevity. Lord Shiva and Parvathi Devi appeared in front of Maha Vishnu and Mahalakshmi and granted their wish but they didn’t give respect to Parvathi Devi. Once Mahavishnu prayed to Lord Shiva to get a child.