More specifically, the Tolkien/Norse thing is because: A) vikings are cool, and B) I want to have elves and dwarves and halflings and I'm at a point where I can't justify their inclusion in a fantasy setting unless it's either overtly Tolkienesque or overtly based on the folklore Tolkien ripped off (in this case I'll be trying, probably unsuccessfully, to navigate some vague line between both).*
The city is, rather, a trading centre, and was from its inception (around one hundred years ago), having initially been founded by the Wormfang Clan of Northmen as a means of facilitating easy exchange of plundered goods for Dwarvish silver. The Wormfangs are still masters of the city, having repeatedly bested attempts by other clans (not to mention orcs, goblins, and the enigmatic fugus-creatures which occupy the furthest peaks of the mountains) to take it by force. Such attempts have tapered off in the last few decades, ever since Jarl Steppen Thigh-crusher opened up the city to "all honourable peoples" (which includes all Northmen clans and most other men, as well as elves, dwarves, gnomes, halflings, and the serpent-men of the Scorching Wastes, but excludes orcs, goblins, fungus-creatures, and most other monstrous-races). Conquering the city seems like a waste of time when it's main value is in the trade opportunities it affords, for which the doors are already open to most.
As such, Silfurfall has become a rather cosmopolitan place. Most of the permanent residents are still Wormfang Northmen, but more than half of the population at any time is comprised of folks from elsewhere, including a significant number of non-humans (more than in any other human-controlled city). Many of these are merchants and craftsmen whose main aim is business with the Five Kingdoms, but given the constant influx of goods from all over the known world and beyond, there is always a steady stream of those looking primarily to buy, rather than sell. Moreover, the lands beyond the Silfur Mountains are reportedly littered with ancient ruins, so the city is a popular stopping point for adventurers on their way to search for lost treasures (travel over the mountains is certain death due to difficult conditions and the aforementioned fungus-creatures, but the Five Kingdoms allow passage through their mines - for a price, and only under heavy escort).
Silfurfall has also become a rather dangerous place: large numbers of wealth and goods moving through makes it an attractive haven for thieves, as does the relatively lax rule of law that's settled over the city ever since Jarl Steppen came into power. He's a warrior, not an administrator - he'd rather be off fighting orcs while a handful of his lieutenants oversee the day to day operations of the city. Unfortunately, Steppen has chosen for this task those lieutenants whom he doesn't particularly trust in battle - and for good reason, because they're generally corrupt and willing to overlook all kinds of law-breaking as long as they get their kickback. It's unclear whether Jarl Steppen is ignorant of these happenings, or whether he's aware and just doesn't care.
The city is divided into a number of rough neighbourhoods or districts. Each has an "official" name, but locals and regular visitors more commonly refer to them by a second set of names, which derive from the way people tend to die in that part of the city.
Beheading District (Old City). As its "official" title suggests, the buildings and streets of this central neighbourhood are some of the oldest in Silfurfall, around which the rest of the city grew over the decades. The central square is where public executions of criminals and prisoners take place. It's also where the city guard barracks are located, which makes this one of the safer districts - and as such, its inns are always full, and there are numerous shops and residences.
Poisoning District (Castle District). Right next to the Beheading District, this neighbourhood houses Castle Ormor, where the Jarl resides when he's in town, and where (both in and around) the city overseers and other nobles and elites of the Wormfang Clan make their homes as well. It is, unsurprisingly, also a very safe district, but everything here tends to cater to richer tastes.
Slit Throat District (Market District). There are numerous markets all throughout the city, but the biggest and most varied of them is located here. Correspondingly, it's a hotbed of crime, and the thieves' guild** has its headquarters here. It's also where serpent-men tend to stay when they're in town, as inns and taverns elsewhere are somewhat less tolerant of these most inhuman visitors.
Drowning District (Shipping District). The mighty river Drullavat (which falls from the Silfur Mountains and provides easy access to the ocean) runs through this neighbourhood, and as such it's mostly docks, shipyards, and warehouses, as well as the sort of inns and drinking establishments that cater to sailors and other low-lives.
Stabbing District (Wormfang District). The "official" name refers to the fact that this is where most of the city's permanent residents lie, most of whom are Wormfang Northmen. The unofficial title refers to the fact that these residents are famously prone to bouts of murderous rage at real or perceived slights.
Sacrifice District (Temple District). One of the few rules of which Jarl Steppen insists on strict enforcement is a ban on ritual sacrifice, even of orcs and goblins. As such, this neighbourhood isn't really appropriately titled anymore, but it was such a popular practice for so long that the name has stuck around. The reality is that such sacrifices still happen in many of the district's temples, they're just quieter now. It should also be noted that this isn't the only place to find temples in Silfurfall; they're just the most numerous here, with at least one devoted to each of the gods, and several devoted to the most popular (Thor, Odin, Loki). More than one is actually a front for the worship of what some call "the Oldest Gods," who are known by various names (like Cthulhu, Yog-sothoth, Nyarlathotep... you get the idea).
There should probably be a few more neighbourhoods (I want to do the thing from Vornheim where you write out the numbers of neighbourhoods haphazardly next to each other to get an abstract city map), but I can't think of any more types of city districts or types of death, so that's it for now.
*I've got Elves and Dwarves in Xish, my dying-earth setting, but there I've justified it by making dwarves and halflings Vancian vat-bred slave-races and elves your typical fey bullshit. I'm not super satisfied with this either, and I think subsequent iterations of the setting are just not going to have them at all.
**I'm actually not sure how I feel about that old fantasy roleplaying game standby, the Thieves' Guild, and I reserve the right to replace it with something fresher or just get rid of it altogether.