I am happy to provide more specific sources, but I want to fully understand exactly what you are interested in. I'm not 100% clear but it sounds like you are interested in specifically Northern Germany, Denmark, and Norway/Sweden (non-Celtic Europe) in the Iron Age?

There are going to be a few problems with recommending broad history books:

1. Language Barriers. Once you move into non-Celtic Germany, Denmark, Scandinavia, you are going to be harder pressed to find generally available books that are in English.
2. Age of publication. Even in translation, a lot of books on the topic are old enough to be functionally useless to you.
3. Availability. A quick search for some known titles on worldcat or booksellers shows me that you might have to pay a pretty penny or wait a good while to get your hands on Conrad Englehardt's "Denmark in the early Iron Age" from 1866.

BUT, I'm only throwing these out there because I don't think books are your way to go. I think your solution is to start your deep dive into the world of journal articles! By narrowing down your specific regions and interests (say, metallurgy or burials) you can find articles on exactly what you want to learn about.

If you want (since I know this was a lame duck answer) go ahead and send me a DM with some of your interest and I'll try to get some PDF articles for you.

Malcom Todd's 'The Early Germans' is a good place to start. Guy Halsall's 'Barbarian Migrations and the Roman West' and Peter Heather's various books on the fall of Rome (e.g. 'Empires and Barbarians', 'The Fall of the Roman Empire') touch on the late Roman Iron Age north of the frontier. 'Ancient Scandinavia' by T. Douglas Price is a good, recent Archaeological account which will apply more or less equally well to Germania up until the Late Roman Iron Age. I also recommend 'Iron Age Myth and Materiality' by Lotte Hedeager, although it technically comes in at the end of your period of interest--it reaches back to earlier periods for comparison.

Aside from the books above, there's not a lot of recent quality scholarship on non-Celtic Iron Age Europe in English. Where scholarship does exist, it tends to paint pictures in broad strokes. Read primary sources from the Roman side of the frontier with a skeptical, but not too quickly dismissive, eye. While it is certainly true that Caesar, Tacitus, and Strabo all had slanted and limited views of nothern europeans (which are also seperated by centuries, which can account for a lot of apparent contradiction) that doesn't neccessarily mean they intentional misled or fabricated every detail. Tacitus' aims may have been a bit more socio-commentarian or literary than ethnographic, but Caesar appears to have accounted what he saw, as it seemed to him (from his biased and limited perspective), or what he was told by others, without too much attempt at editorializing.

One thing that could be helpful to note is that you can pretty much toss everything you think you know about Norse religion, at least as it applies to the Iron Age, pre-500 AD. Not many accounts of Northern European religion exist from those periods, but the Viking Gods that we now know are only the survivors of a vast and non-uniform ploytheistic pantheon which was heavily influenced by contact with Rome. The oldest Northern God we have solid proof of appears to be Tiwaz/Tyr, a Zeus/Jupiter sky god analogue who may have been supplanted in later eras by an equally ancient death god (Wodan) who may have absorbed some of the aspects of Roman Mars and Mithras. The Donar of Caesar's era may well have become the later Thor, but beyond that, direct analogies are difficult.