Due to Loki's nature as a trickster, among many other reasons, I believe he was demonized with the spread of Christianity in Scandinavia and associated somewhat with Lucifer/Satan (please correct me if I'm wrong). Did anything similar happen with Odin, as his involvement in seiðr and other magics could have been seen as satanic, or was he equated more as a Christ figure (i.e. hanging on Yggdrasil) or God equivalent (Allfather)?
Any information helps. Thanks!
As a rule of thumb, Christianity demonized all old gods (even the benevolent ones) to give people more incentive to worship only the Christian god and no one else.
The big problem is that basically every written evidence of Odin or any other Old Norse god was written by a Christian monk, which inherently biases everything we know about Odin. Even the Edda, which is the source of most of our understanding about Old Norse religion, was written by a Christian monk. You have to keep in mind: even if said monk had the goal of documenting this old religion as truthfully as possible (which we don't know, he might have deliberately changed stories according to his taste or belief), he couldn't possibly risk appearing heretical by casting these non-Christian gods in a too favorable light.
We don't have any contemporary texts that tell us about how Odin was viewed or worshiped before Christianity reached Scandinavia, so we cannot tell how his image changed with the arrival of Christianity. There may be some objects left of that time like carved stones or wood fragments, but that doesn't tell us much about how people thought about the old gods. Yes, there was a runic script, but that was mostly used to commemorate the achievements and lives of real people. Scandinavians simply never had a tradition of writing down anything about their religion and traditions. Even early Christians mostly wrote about the culture of other people and not their own.
Maybe this question can guide you to more information.
Questions concerning Christian influence on Norse mythology are always hard, given that many of the written sources at our disposal were compiled after the Christianization of Scandinavia. Nevertheless, cross-referencing with the archaelogical record and with the pre-Christian sources has allowed scholars to reach some consensus on tales and motifs which are genuinely pagan. However, characters like Loki, and events like Odin's sacrifice to himself remain controversial, and are still debated today.
Even though your question concerns mainly Odin, I believe also the opening sentence about Loki deserves some clarification. For this reason, I will split my answer in two parts, one for each deity.
It is entirely possible that Loki underwent a 'demonization' after the Christianization of Scandinavia (this is a view held, among others, by Jan de Vries). This would explain his apparently contradictory nature:
On the one hand, Loki is said to be the murderer by advice (ráðbani) of Baldr, whose killing is said to be the worst incident among gods and men (Gylfaginning, ch. 33). Both Loki and his children play a central part in Ragnarok on the side of the enemies of the gods, and many other calamities that strike the gods are caused by Loki, too. On the other hand, he is the blood relation of Óðinn and a figure who, by his own will or not, brings the gods some of their most precious objects, without which they could not fulfill their function as defenders of the cosmos.
Jens Peter Schjødt, entry on Loki in Medieval Scandinavia: An Encyclopedia
However, not all scholars share (or shared) this view. For example, Georges Dumézil, in his book Loki (1948), argued convincingly in favor of a purely Indo-European (that is, not influenced by Christianity) origin of Loki, and compared the murder of Balder to a similar episode appearing in the Ossetian Nart Saga, involving the trickster Syrdon and the hero Soslan.
On the opposite side of the spectrum, Kees Samplonius, building on an etymology proposed by Sophus Bugge, which derives Loki from Lucifer, believes in a purely Christian origin of Loki:
However, if Loki was a god (or at least a supernatural being of some sort) with the character of Satan and with a name best explained as short for Lucifer, strong arguments are needed to make him an Old Germanic deity. [...] The only sensible answer is that, for all of the variances of manifestation, Loki drew his name from the Christian Lucifer and remained associated with him in various ways. [...] The heathen or merely superficial Christian Nordic people may have liked this Lucifer derivative, because the figure was suitable for good story-telling, just as the Devil figures in many popular tales in the rest of Europe.
Kees Samplonius, The Background and Scope of Völuspá, in The Nordic Apocalypse
All this to emphasize the difficulties in assessing to which extent a complex character like Loki was influenced by the process of Christianization. In the words of Jens Peter Schjødt:
We have seen that most of the research concerning Loki has focused on attempting to distinguish between pagan and Christian notions of the figure. This is reasonable given the nature of especially the literary sources we have at our disposal; but at the same time, there is a risk that the quite trite acknowledgement, known to all historians of religion, that all religious notions and all religious rituals are to some extent influenced by something else, is forgotten, resulting in the utopian idea that if we are only careful enough in our treatment of the sources we can find, behind all those late and foreign influences, a figure that was pure and not ‘polluted’ by any sort of influence. Such a god does not exist, not in Scandinavia, nor anywhere else, at least not within the whole of the Indo-European and Semitic areas.
Jens Peter Schjødt, Loki in The Pre-Christian Religions of the North
In Odin's case, the situation seems to be slightly simpler. There is some consensus among scholars regarding an original 'demonic' nature of Odin, associated to his close connection with the dead and with human sacrifices, as well as to the practice of various forms of magic. For this reason Dumézil, in Gods of the Ancient Northmen (1973), proposed a parallel between Odin and the Indian god Varuna.
Odin's demonic nature is exaggerated whenever Odin interacts with Christian characters, and certain Christian authors tend to portray him in a negative light:
We also meet Óðinn in some of the other sagas of Heimskringla, particularly in relation to the missionary kings, Óláfr Tryggvason and Óláfr Haraldsson, although there he is portrayed as demonic. [...] In Gesta Danorum, Óðinn is quite frequently mentioned in the first nine books, often in a way that is clearly hostile from the perspective of the author since Óðinn, more than any other god, is seen as a representative of the pagan religion. [...] He is, for example, ridiculed in the Rinda episode (and is expelled by his own people afterwards) [...] In another episode (Gesta Danorum 1.7.1), he is so embarrassed that his wife, Frigga, has committed adultery with a servant in order to acquire some jewellery from a statue that he goes abroad afterwards. [...] Also in some of the konunga sögur, dealing with Christian kings, we meet this motif, albeit in a transformed variant: Óðinn tempts the Christian king with his knowledge about the past or he offers something to the king (which must of course not be accepted), a motif we also find in Hrólfs saga kraka.
Jens Peter Schjødt, Óðinn in The Pre-Christian Religions of the North
The myth of Odin hanging from Yggdrasill lends itself to different interpretations. Some scholars consider it a genuinely pagan myth (perhaps associated to shamanic or initiation practices), which made Christians uncomfortable:
Snorri clearly knew the myth of Óðinn’s sacrifice of himself to himself on Yggdrasill, but it is never mentioned in Snorra Edda, probably because its obvious resemblance to the Crucifixion story would be likely to make it seem blasphemous.
John McKinnell, Heathenism in Völuspá in The Nordic Apocalypse
Others, like Annette Lassen in her article The God on the Three, see in this myth an attempt by a Christian author to portray the "doctrine of paganism as misunderstood or inverted Christian doctrine". Regardless of the interpretation, it is safe to say that the myth of Odin's sacrifice to himself was never used to equate the god to a Christ-like figure.
Finally, I would like to address the attribute of 'Allfather' associated with Odin. While this attribute alone may not suffice to equate him with the Christian God, it could have played a role, alongside other features of the Norse god and his cult, in facilitating the conversion to Christianity by the rulers of Nordic countries. This idea is brought forward by Terry Gunnell in From One High One to Another: The Acceptance of Óðinn as Preparation for God.
