Why are the Julian calendar months named after Roman gods/emperors but the days of the week are all variants of Norse gods?
These are not Norse Gods, per se. The names of the gods associated with the days of the week have been localized to refer to Germanic gods instead of Roman gods, with the exception of Saturday. Interestingly, the name Sunday was preserved, with its reference to the sun as it is in Latin, diēs Sōlis (the Day of the Sun), as opposed to the modern Romance name diēs Dominicus (the Day of the Lord). Showing that it was adopted before the shift in nomenclature to reflect Christian values in the Roman Empire.
We, unfortunately, don’t know that much about the Germanic pantheon. By the time we start to have references to Germanic mythology, late 1st millennium, early 2nd millennium, these peoples have been in contact with the Romans for about a thousand years. So what we do know has been heavily influenced by the Romans. Both early Roman paganism and Roman Christianity.
At some point, about a thousand years earlier, in the 1st century, speakers of West Germanic languages began to equate Roman gods with their own gods. We don’t exactly understand this process, but it led to the establishment of a 7 day week with names that had correspondences between Roman and Germanic gods.
It’s unclear how much of a stretch this was. It seems like the very distant origins of both religious traditions was Proto Indo European, but the extent to which you can just say “Thor is Jupiter” is enhhh.
Nevertheless, that’s what these folks did, through a process known as interpretātiō germānica. And that’s how they named their days of the week. And that’s part of the reason why it’s hard to pick apart Germanic or Norse mythology, because obviously, at least in certain more literate sectors, they had been equated with other religious systems for centuries.
Beowulf was written down by a Christian! Though the debate as to how accurately it represents pre-Christian paganism is a huge debate, it was definitely affected by this perspective. Similarly, the Norse Edda was recorded in the 13th century and there were definitely already Norse Christians by this point.
Now, on the other hand, the days of the months were not influenced by Roman nomenclature until later on and spread with the influence of the Roman Christian church throughout the first millennium AD. Germanic month names in English were common until the Medieval Period, but they lasted longer in other Germanic languages.
The names of the months we use now were actually borrowed directly from Latin and replaced the Norman French terms used during Middle English; January is a lot closer to Latin Iānuārius than French Janvier.
In short, the adoption of Roman months came later than the adoption of Roman days. And by the time Roman months were being adopted, Latin had already been introduced via Christianity and so, there was no need to localize the names.