Viking mouthwash use would have been remarkably similar to the act we know and love today, with a few minor - yet important - caveats:
1) Vikings would use only mint or original Listerine. No less harsh citrus flavors or lesser name brands.
2) Vikings would refuse to "swish" anything round in their mouths. Instead, the user's head would be violently shaken from side to side - as if he had just used his teeth to rip off the ear of an enemy.
3) In the absence of mead, mouthwash could occasionally be imbibed.
The rest is identical to our current methods, excepting of course the use of skullcups.