It is typically assumed that when similarities are found between Christianity and another religion, whether in myth, dogma, or practice, the flow of influence is syncretism into Christianity. This tendency is largely due to the many instances of Catholic hagiology (mythology about the Saints) appearing much like myths from earlier pagan times before Christianity had heavy influence over the area.
There is very likely some level of influence, however, it is Christianity that influenced myths about Loki.
The earliest Norse myths involving Loki portray a character that is certainly a trickster, but not malicious. There are many instances of Loki engaging in a good deal of intentional mischief, but also resourceful and helpful, giving inventions to humans, and eventually resolving his mostly harmless mischief. However, by the 10th century, after nearly 200 years of significant Christian influence, Loki's myths make him out to be a much darker character. In a myth involving a character named Baldr (who was certainly influenced by Christian depictions of Jesus), Loki is an evil specimen that murders Baldr out of jealousy.
When they capture Loki, he is held in a prison until Ragnarok (the Norse apocalypse that was also likely influenced by Christianity) and tortured by having a perpetual stream of snake venom drip into is face.
Loki's evil nature and jealousy (of a Christ like image especially) and his ultimate tortuous imprisonment was undoubtedly influenced by Christian perceptions of Satan. In Christian mythology, Satan is evil. And the eschatology (apocalyptic theology) revolving around him involves an eternity of torment, which is undoubtedly because of his heinous misdeeds against God, humanity, and the rest of creation.
This progression for trickster gods to take on a darker persona as the centuries pass is actually quite common (Satan in Job, for example, is not necessarily evil, but is certainly an accuser and adversary, but by Revelation he is patently evil). It is therefore expected that Loki would become more like Satan as Christianity influenced the Norse mythos, because Satan had already progressed into a personification of evil centuries earlier. Without Christian influence, Loki still likely would have become more evil and less trickster, so the rising influence of Christianity in Norse areas and Loki's conversion to an evil character may have been coincidental, however it does seem likely that Christianity at least hastened the process.
- Lucifer: The Devil in the Middle Ages - "The parallels between Loki and Satan are striking but are for the most part Christian coloring of paganism rather than the opposite."
- The Trickster, the Devil, and an Ambiguous World - The Anthropik Network [Web Archive] - "It’s fairly easy to divide stories about Loki into two historical categories: pre-Christianity, and post-Christianity."
- A Brief History of the Vikings - "By the [10th century], Loki had perhaps been influenced by several centuries of Christian lore, and was now seen as a far more devilish figure that he may originally have been."
- Archetypes and Motifs in Folklore and Literature - "Tales of Loki's evil and binding are clearly influenced by the later Christian identification of Loki and the Devil (tricksters, perhaps because of their profane character, are often equated with the Devil if their original culture is converted to Christianity)."
- Völuspá - New Advent - "Balder, the innocent god, is treacherously slain through the machinations of the wicked Loki." and "Christian influence is not only possible, but certain."
- Viking Religion - BBC History
- A New Place for Loki, Part II on Polytheist.com states that "since Loki was a deity who I believe was originally responsible for carrying burnt sacrifices to the gods and freeing the souls of the dead via cremation, it is only natural that the Catholic Church would have found him particularly deplorable." There are many sources for the article, but I have not looked through them. There is a certain level of sense to the claim, but without vetting it, the source finds itself in the notes section instead.
- Christmas in Germany: A Cultural History states "The Norse God Loki [et al.] ... contributed to Elm's syncretic descriptions of Christmas custom." A different topic, but interesting.