The torc/torque and Viking age arm ring are not synonymous, a torc which was worn by the ancient celts is a ring of twisted circular metal open at the front and predominantly worn around the neck, though the torc design could also be worn as a bracelet or around the waist. The word torque is latin and literally means to twist, its use as a word for a metal neckring is modern (19th C). Here is the full etymology and usage:
torque | Origin and history of torque by Online Etymology Dictionary
To the Celts the torc/torque, as a neckring, was a symbol of power and authority, one of the most well known torcs is depicted on the Gundestrop Cauldron adorning Cernunnos.
The Viking age armring was predominantly worn by men but they have also been found in female graves. The armring was of varying designs, made of gold, silver or bronze depending upon your wealth. It was a decoration, a symbol of wealth and status, the armring could also be cut up into peices, weighed and used as currency; for this reason armrings are also called ring money or hack money.
I doubt it matters what arm you wear it on, probably on which ever arm does not impede your movement or get in the way. You might enjoy this article:
Thegns of Mercia: Arm Rings
The Viking age oathrings are a different matter these were cultic rings upon which oaths were made to chieftains and gods, they were not decorations. Oathrings are mentioned in the literary corpus, both Norse and Anglo Saxon. Here is an article for you.
Performing Oaths in Eddic Poetry: Viking Age Fact or Medieval Fiction?
I hope this answers your question.