A Larp association in this context is basically the organiser of an event.
There are a couple of different ways to organise a Larp event. You can structure it as a business, where the players are clients that buy the right to play in your event, or you can organise in an association, where the players (and NPC's and GMs) are members of that association, paying contribution.
Each association defines their own rules. While there might be a lot of overlap between different associations and events, these rules can still vary greatly. Each association also writes their own story for their own events.
As an example, I personally play and organise a Larp named Charm. The organisational structure behind this is an association, also named Charm.
Group is used pretty much interchangeably with event/organiser.
As I said, many organisations use fairly similar rulesets. Rules can be grouped together in a system if they are mostly similar.
Never heard of them, but a quick google search leads me to believe that this would be a Larp Association.
From their own website:
Nordic-style larp, or Nordic larp, is a term used to describe a school of larp game design that emerged in the Nordic countries. Nordic-style larp is dramatically different from larp in other parts of the world – here are a few examples of aims and ideals that are typical for this unique gaming scene:
Immersion. Nordic larpers want to feel like they are “really there”. This includes creating a truly convincing illusion of physically being in a medieval village/on a space ship/WWII bunker, playing a character that is very close to your own physical appearance, as well as focusing on getting under the character’s skin to “feel their feelings”. Dreaming in character at night is seen by some nordic larpers as a sign of an appropriate level of immersion.
Collaboration. Nordic-style larp is about creating an exciting and emotionally affecting story together, not measuring your strength. There is no winning, and many players intentionally let their characters fail in their objectives to create more interesting stories.
Artistic vision. Many Nordic games are intended as more than entertainment – they make artistic or even political statements. The goal in these games is to affect the players long term, to perhaps change the way they see themselves or how they act in society.
This isn't a single event, but rather a style of events, a system.