Like if you were from one of the towns named after Tyr or Odin or Thor, were you most likely going to be in a regional cult that specifically worshipped that deity over the others? How much was the Norse pantheon actually a coherent interconnected story canon to the average person at the time? And how much was it just different groups of people in different regions that worshipped different things, kind of all just letting their lore blend together and combining individually-developed regional myths into a broader story over time?
For instance do we know that Thor was always considered Odin’s son, or is it possible that the people that developed and worshipped Thor started interacting with the people that worshipped Odin, and instead of fighting about it they compromised with “well maybe they were related” and it went from there?
And really I’ve always wondered if this applied to all of the other polytheistic pantheons too. How much did people on the ground at the time actually care about the broader overarching mythology, and how much was it a case of different towns and groups with different myths that developed independently, which were then retroactively combined into one canon as a compromise? Do we know of any times where perhaps a conquering ruler would recognize all of the different myths and deities as being part of the same broader story as a way to appease the different religious sects and cults that would otherwise have been at odds with each other?
And is it possible that lots of people weren’t necessarily “polytheistic” at all and it’s just historians looking at evidence of lots of different deities being worshipped at the same time and concluding that everyone must have worshipped or treated everything as canon? Like is it possible that Roman historians looked at all the archeology and history dedicated to the various Greek gods that people worshipped and came to the conclusion that it was a much more coherent interconnected mythological universe than it actually would have been to the average Greek person at the time?
While we know basically nothing about actual Norse religious practices (every written source we have was written by Christians who either converted from Norse paganism, Christian missionaries who went to Scandinavia and probably didn't have the best opinion of pagans to begin with, or the handful of monks that actually managed to survive Viking raids and may or may not have just escaped from a life of slavery in Scandinavia (who, given that experience, probably despised anything to do with the people they saw as bloodthirsty barbarians). Given this, it's pretty unlikely that "accuracy" was the first thing on their minds. At best it's a case of "these stories are quite silly" and at worst it's "they can either convert or die." The few, and I mean very few, non-Christian sources come from Muslim travellers who encountered the Kievan Rus, which it is debated how any of their practices were Scandinavian in origin and how much was Slavic syncretism.
Our best sources for typical practices for Germanic paganism would probably be the also pagan Romans, which is well before the Viking Age and who themselves also didn't care much about accurate anthropological records as opposed to "Hey, you're a tribe that exists! Also, we own you now and by the way, your gods are really our gods so please be good because by extension our Emperor is now part of your pantheon. If you are not good, ask Carthage and Jerusalem what happens." However what Roman records do exist seem to have a very different cosmology than what we see in Medieval sources, with Woten (aka Odin) being basically nonexistent for at least the first few centuries after contact, and Þunarr (aka Thor/Þorr) being in his place. Whether this was intentional by the Romans to make it appear that they also venerated Jupiter as they did, the Germanii and Alemani tribes simply didn't recognize Woten, or the Germanic pagans had a religious upheaval around the first century BCE is unknown. Afterwards Roman sources equated Woten with Mercury (Was it because they're both trickster gods? Was it because they were both wanders and psychopomps? Who knows!).
However as far as practices are concerned we do see the Romans include such notes as the Germanii revering idols and performing animal sacrifices (riveting and unusual, I know. Totally not what nearly every other religion on the planet was doing at the time except the Jews and Zoroastrians, who both rejected idols, and the Jains who rejected killing animals). Rather than idols of marble or gold, which access to was quite limited in Germany and I'd imagine even moreso in Scandinavia, the idols were almost always carved from wood, and occassionally hewn from non-precious stone, and very rarely silver. Amulets for religious symbols such as Þunarr's hammer/axe (some sources say it was an axe and not a hammer, which shows a possible closer relation to the Slavic pantheon where the chief god Perun, also a thunder deity, wielded an axe) were carved from stone or bone, with some surviving up to today, were being traded through the Roman commercial networks. While wood is almost definately not going to survive for thousands of years, we do see a very small handful of stone idols in artifacts discovered in the past few centuries. We also see Medieval sources, particularly those chronicling Charlemagne's conquest and conversion/genocide of the Saxons also detailing this same practice, so it is highly likely that wooden idols played a large part in Germanic paganism. Whether this is because wood had an especially sacred role in their rituals or just because it was literally everywhere we don't know. Anybody who did know either converted to Christianity and buried their pagan roots or were slaughtered like pigs by rampaging proto-crusaders.
Besides these fragmentary records of sketchy-accuracy at best, our best bets would be to look at what we know of other polytheistic religions of the Indo-European archetype. You had mentioned the Greeks (who, contrary to your hypothesis, did not need help from Rome to record their own religious beliefs, they handled that abundantly by themselves) and they are the perfect place to start. The different city-states of Greece retained slightly different interpretations of the myths and gods, for example Sparta and Crete were seen as the weirdos of the Hellenic world for viewing Aphrodite as a war goddess as well as a love and sex goddess, because her worship was imported to Crete and Sparta first from the Phoenician peoples who worshipped Ishtar, the goddess of love, sex, and war. The rest of Greece dropped the war aspect from Aphrodite and referred to the Spartan variant as "Aphrodite Area." This was a major source of contention between Cretan/Spartan worshippers and the rest of the Greeks, and this theological conflict can even be seen in the Iliad where Homer blatantly has Zeus tell Aphrodite that the battlefield is no place for a woman like herself (while also ignoring Athena being on the battlefield) and scholars from other parts of Greece claiming that the Spartans saw all the gods as war gods while historians from Sparta or who decided to live in Sparta (e.g. Xenophon) reiterated that, Sparta only venerated three major war gods, Ares, Athena, and Aphrodite Area. There were other minor war deities like Phobos and Diemos, and Thanaton played a minor role in war as well (because when you have a battle people tend to die, so the god of Death has to come up to Thermopylae and do his job of collecting them. I'd imagine if the Greek gods were real, Thanaton would hate the Spartans for causing him so much extra paperwork... papyruswork?), but they were rarely venerated or invocated.