Hello historians and laymen!! I have searched this subreddit for a similar question, and there is one, but it is asking about Vikings & Muslims & Mongols, and only ever Vikings & Muslims was answered.
If my horrible understanding of history is correct, at some point those two cultures existed at the same time (I think). I believe they may even of had similar times for their golden ages?
EDIT: Here is a gift for your time, a song with Viking nature:
The Viking period is commonly defined as between 793 and 1066. There is some debate about the exact definitions, but definitely between the late 8th and 11th century. The Mongols started their expansion out of Mongolia with Genghis Khan in the early years of the 13th century. So no, there was no Mongol-Viking encounter.
They did meet the Turkic-speaking peoples of Southern Russia, though.
I think the closest thing to a Mongols VS Vikings deal was when the Mongols took over Russian territory. There were people whose ancestors of couple generations back that were Vikings.
Other than that, Vikings as far as I understand, assimilated and changed their culture fairly quickly to the nations they presided in.