One of the more readily apparent ways it's influenced us would be the names of the days of the week in English. We have Tuesday, derived from "Tīwesdæg," or "Tiw's Day," Tiw being the Old English cognate of the Norse Tyr. Likewise, Wōdnesdæg for Woden/Odin's Day, Thursday perhaps most obviously of the lot derives from "Thor's Day," etc.

Now, these generally derive from Old English rather than Old Norse, going back the migration of Germanic tribes into England. I don't know if that falls within the scope of your question, by your view, but the Anglo-Saxons and the Norse had a lot of overlap in their mythology and culture, being derived from the same general sources.