There are organisations in the Empire that have grown in influence beyond the confines of a single nation. These organisations are collectively referred to as Imperial sodalities. They are associations or societies that have a common purpose and sufficient reach or influence to be relevant to the Empire as a whole - but they are not a direct extension of the Imperial government like the Imperial Conclave or the Imperial Synod. They do not receive any logistical assistance from the civil service and most do not benefit from ongoing financial assistance from the Imperial Senate.
A sodality is any organization in the Empire that is eligible to citizens from more than one nation. Most sodalities are minor in nature and have no legal status or significance. If Imperial citizens meet up to share different nation's cookery recipes, their organization does not have or need any legal status. They are free to set their own rules and to do as they please within the limits of the law.
A sodality gains legal status when it's existence is recognized and codified under Imperial law which requires a Senate motion. Some of the most important sodalities in the Empire are the Imperial militia and the various Conclave orders, all of whose existence and operation is governed by Imperial law.
Creating a Sodality
It is not possible for players to create a sodality as part of character creation - the banners, sects and covens that new players can create are based in the nation they choose to play, but the definition of an Imperial sodality is a group with a reach or scope that extends beyond a single nation. Creating an Empire-spanning organization is something that must be done in play - not as part of character creation.
To create a sodality in play, you simply need to create an organization and have people want to join it. The sodality will not be listed or described on the wiki - it is up to you to promote your sodality in play.
If you want your sodality to have legal status - even if that is simply to have its existence recognized by Imperial law - then you will need to have its existence formally acknowledged by the Imperial Senate using a Senate motion.
The Imperial Senate can create a sodality or recognize the existence of own by passing a suitably worded Senate motion. The simplest way to do this is to create a new Imperial title whose responsibilities include representing or leading a sodality. This may be implicit in the wording of a motion - for example in 377YE, the Senate passed a motion to create the Captain of the Senate Guard. Implicit in the description of this title is the existence of a sodality - the Senate Guard - and that the new position will assume responsibility and leadership of this sodality.
Under most circumstances, this is all the detail that is required. Provided that the Senate is comfortable to delegate the operation of a sodality to others then nothing further is required. If the Senate wishes, they may allocate funds to support a sodality - but only by granting a stipend or disbursement to a specific citizen - usually whatever title has been created to be responsible for the sodality. Any Imperial sodality linked to an Imperial title will be described on the wiki page for that title.
A Senate motion that creates a sodality by appointing a new Imperial title to lead it, is assumed to grant that title authority to determine who is and is not a member of the sodality by default. This is the only legal power automatically conferred in this way. These titles do not have legal authority to issue orders to Imperial citizens or restrict what they can or cannot do. In the example of the Captain of the Senate Guard - they have the legal power to specify who is and is not a member of the Senate Guard, but they do not have the legal power to enfore any orders or instructions they give to members of the Guard.
If the Senate wish to go further then it is possible to create laws that dictate how a sodality will operate or who can join. Such laws are carefully scrutinized by the Constitutional Court to ensure that any benefits are proportionate to the loss of liberties by Imperial citizens.
The influence of most sodalities that are created in play does not extend beyond Anvil. NPCs do not typically join these sodalities and their influence is based solely on the players who join them at events.
It is possible to extend the influence of a sodality beyond Anvil by creating an appropriate commission, usually a sinecure, ministry or great work, but potentially anything. The larger the commission, the greater the influence it will tend to have. For example the Dean of the Lyceum is the Imperial title associated with the Lyceum, a college of magic situated on an island east of Siroc. Membership if the Lyceum is open to magicians from across the Empire, so it is a sodality.