From Odin hanging from the World Tree and taking a spear in the side to formation of humans from natural matter, there seem to be a lot of similarities between old Nordic tales and common Christian themes. Can we know how much the Norse influenced Christianity, and vice versa?
The important thing about Norse mythology is that nearly everything we know about it was written down long after the Scandinavian conversion to Christianity. Denmark, Norway and Sweden finalised their conversion through the establishment of their own archdioceses in 1104, 1154 and 1164 respectively, and it had taken up to two centuries for Christianity to fully take root, especially in fringe communities, this was often because of the centrality of some Pagan beliefs to the legal system and some cultural elements, and the recording of earlier Norse mythology was in part an element of the codification of custom and lore for legal purposes by Christianising authorities. By contrast, Snorri Sturluson's Prose Edda isn't written until the 1220s, and the Codex Regius is estimated to be thirteenth century although it's only known from the seventeenth century onwards.
If you read contemporary Christian texts about pre-conversion Scandinavia, such as Adam of Bremen's Gesta Hammaburgensis Ecclesiae Pontificum, written *c.*1073-1076, it rapidly becomes clear that they know absolutely nothing about Norse Pagan religion, lore or cultural practice, and indeed most of Adam's assertions have been proved false by archaeology. Some of his text is just lifted from Pliny's Historia Naturalis.
The Christian faith does pick up some cultural practices and also lexicon from Pagan communities, but these are usually proto-germanic, and absolutely cannot be said to be lifted from specifically Norse mythology. "Hell", for example, replaces the Judaic concept of "Gehenna" as the place for punishment sinners, but contrary to popular belief, is not lifted from the Norse Hel, appearing as a term in post-conversion England long centuries before the arrival of a substantial Norse cultural influence. Rather the two share a proto-Germanic root, to redescribe a Judeo-Christian concept in a means more familiar to a culturally Germanic audience. In a similar vein, int's an oft-repeated lie that Easter is stolen from the Anglo-Saxon goddess Eostre. The actual Christian term is paschal, originally deriving from Hebrew, and 'Easter' derives from Bede explaining to his audience that this Christian festival is broadly-speaking similar to the Eostremonađ with which their ancestors might once have been familiar, spring renewal celebrations being a cultural constant in a great many global cultures and societies, for obvious reasons.
What this means is that, rather than Christianity be influenced by Norse mythology, it's highly likely that what we think we know about Norse mythology is in fact influenced by the Christian writers who recorded it, perhaps filling in missing elements or changing details as seemed fitting to bring things more into line with their preconceived religious mythology and practices. It would also aid more rapid conversion for the Scandinavian population if their prior beliefs could be depicted to broadly align with Christian beliefs and practices.
Some reading:
Abram, C. (2011), Myths of the Pagan North: The Gods of the Norsemen
Andrén, A(2005), "Behind "Heathendom": Archaeological Studies of Old Norse Religion"
Hultgård, A.(2008), "The Religion of the Vikings"