Note that the sources on North mythology are quite thin. What I'm talking about there is based on the Edda, written about 1000 years later in an other corner of the Norse world by a Christian monk. The religion the Romans encountered doesn't have to be all that similar. Maybe it is, but there isn't much information there to compare. We have a lot more information about the mythology of the Greek and Romans.
What we do know is that the Romans had a tendency to equate the gods of other peoples with their own, both to integrate the religions and as a quick way to describe them to the readers at home. The works of Cesar, Tacitus and the others were written to be read by the educated people at home buy they probably weren't interested in the finer theological differences.
Zeus and Odin were the kings of their respective pantheons but their similarities basically end there. Zeus is a weather and sky god. Thor was at least partially responsible for weather, especially thunder and lightning. (Rupke, The Religion of the Romans +Edda)
Odin on the other hand is mostly associated with wisdom, healing, death, royalty, the gallows, knowledge, war, battle, victory, sorcery, poetry, frenzy, and the runic alphabet. (Edda like I said)
I think you would agree that most of them aren't what one would consider Zeus' domains.
Mercury is considered to be the god of financial gain, commerce, eloquence, messages, communication (including divination), travelers, boundaries, luck, trickery and thieves. His stave is the Caduceus, the one with the snakes that is a symbol of medicine to this day. looks a lot like the Rod of Asclepius, a symbol for medicine.
(Rupke, The Religion of the Romans)
He was probably what fit the closest in the mind of the Roman author and we don't know what aspects of Odin he or the locals that worshipped Odin thought to be the most important. As about all Norse gods are war gods in some way that probably wasn't that important. Odin is much more of a trickster archetype.
One a side note, Tacitus seems to have equated probably Thor with Hercules. It fits with the blunt instrument (the South Germanic version of Thor, Donar, was sometimes depicted with a club, like Hercules, instead of an hammer) and heroic behaviour.
Before diving into this, it's crucial to highlight an important process, an approach to the deities of others known to scholars as interpretatio. In this cases, we're dealing with two types, interpretatio germanica and interpretatio romana. In the former case, the ancient Germanic peoples interpreted Roman deities in line with their own and in the latter process Romans equated their deities to others that they encountered. This was usually performed by way of some perceived resemblance.
Every day English speakers encounter a prime example of interpretatio germanica by way of English weekday names. With the exception of Saturday (a mystery), each day of the modern English weekday refers to an Old English deity: Moon's Day, Tīw's Day, Wōden's Day, Thunor's Day, Frea's Day, and Sun's Day. You may know these deities best not by their Old English forms but by their linguistic siblings (cognates) in Old Norse, Máni, Týr, Odin (Óðinn), Thor (Þórr), Frigg, and Sól.
These Old English and Old Norse deity names descend from a common Proto-Germanic form, which Germanic philologists, a type of historical linguist specializing in Germanic languages, quite easily reconstruct by way of the comparative method.
The Proto-Germanic and Latin correspondences are as follows:
These Latin weekday names are themselves a result of interpretatio romana, wherein the Romans equated their own deities with ancient Greek deities. The ancient Germanic peoples equated Jupiter with who we today call Thor no doubt because of their shared association with thunder and storms (Proto-Germanic *Þunraz literally means 'thunder' and is not only a well-attested theonym, best known to us today Thor, but is in fact the source of the English word thunder—Old English thunor > Modern English thunder). Their common use of thunder weapons, which is a frequent motif among Indo-European deities of this type, may well also play a role here.
While the ancient Germanic peoples equate Thor (or more specifically *Þunraz ) with Jupiter here, sometimes Latin-writing authors appear to refer to the god as Heracles, probably due to *Þunraz having a weapon, likely a hammer-like object, perceived as similar to Heracles's club. This occurs widely, including in Tacitus's Germania. Odin appears to consistently be referred to as Mercury by way of this process, and there are quite a few inscriptions in areas with ancient Germanic peoples who left behind Latin inscriptions invoking these deities (you can find many of these in the handbooks discussed below).
Behind all this is an entirely different but certainly related discussion—some of these actually stem form the same basis. This is undoubtedly the case with *Tīwaz, Jupiter/Jove, and Zeus, as well as host of other deities among other Indo-European language-speaking peoples, but that's a bit off topic and while the Romans and Greeks certainly expressed awareness of a commonality, the Romans do not appear to have considered *Tīwaz as connected, raising further questions about this generally mysterious deity.
As for Odin, there's a been a lot of discussion about his role among the ancient Germanic peoples and if he for some reason supplanted *Tīwaz as a 'head' of the Germanic deities at some point early on but all we can say for sure is that he was an important deity during the Proto-Germanic period and beyond. Thor was by all indications incredibly popular during the Viking Age and appears to have always been so, even back to the Proto-Germanic period.
For general discussion on the ancient Germanic peoples, I recommend both of these tertiary sources (but beware Simek in particular presenting opinion as fact):
If you'd like to read more about comparative material within the Indo-European sphere, the best place to start is probably something like:
You'll also find the following handy for context:
And, finally, if you want to pull up some Proto-Germanic forms, you can always turn to the (full) Oxford English Dictionary or for example a lexicon like this one:
Enjoy!
Edit: Typos