If there's not an official list we can talk about it. As usual it comes down to how the definition is structured. You cant really use geography as the primary filter since roles change as house forces move around (Council is the law in the systems they control, but so are Outcasts and Corsairs). You cant really use piracy as the primary filter either, since that would make all the corps that pirate each other semi-lawful.
So rather than define semi-lawful, maybe define lawful/unlawful and see what falls out. The simplest filter for "Lawful" is if the ID says "Cannot participate in unlawful actions" or at least strongly implies it. Likewise, the simplest filter for "Unlawful" is if the ID allows piracy of the general population without any kind of restriction (ignoring ZOI). Factions that can attack specific enemies are not counted in the Unlawful equation since they cannot attack the general population. That leaves Semi-lawful as the factions that do not fall within either group, being able to kill and/or pirate portions of the general population or having some other restrictions (which may include geography, but ignoring ZOI as a geography restriction).
Using that filter, Council and CR are Lawful since they fall under that filter, while Outcasts et al are flat-out Unlawful. Junkers, GJ, Hogosha, and UC are semi-lawful since they can engage in some limited unlawful activities. Zoners are lawful by virtue of the fact that they cant shoot anybody except in limited situations. Freelancer ID is semi-lawful since they do not have the lawful filter but can only kill and pirate when contracted to do so. K'Hara/Wild are fully unlawful without remorse, using this filter.
Now some odd-balls... Hellfire cannot engage the general population at all, so they are not Unlawful, and in fact appear to be Lawful since they cant hardly attack anybody except Liberty lawfuls which is the same as Rheinland Military et al. Bretonia Privateer cannot kill/pirate the entire general population at will so they are not generally Unlawful, but they can kill/pirate enough of them to warrant Semi-lawful status. Reapers of Sirius could also be considered semi-lawful by their restriction on joining active fights. Coalition ID has the magic "May not engage in unlawful actions" phrase but that comes after "Can destroy ships that are affiliated with enemies of the Coalition," and since Coalition is hostile to all the houses that basically means the global population minus some allies, so they are fully Unlawful in my book.
ps--there is an interesting inverse distinction here, which is that most of the lawfuls can hunt pirates/terrorists, which prevents them from hunting semi-lawfuls. That puts this topic under the realm of "rules" so I was hoping there would be an authoritative list.
I believe the current way they are classified is listed on the draft Technerf/Rephack chart. Alternatively, there is some indication in the grouping of the Wiki ID list.
You've got a fairly ok system, and it fits this with a few "because it makes sense" alterations with the conflicting cases.
I'd generally classify them as what they are viewed as in their house:
All Police, Military, Special Forces and House Corporations are House Lawful.
All factions based in the house they fight against (including HF) are House Unlawful. The Council have moved out from Gallia now, so I would not included them in that. I'd probably classify them as semi-lawful, although for grouping rules it'd be "Military".
Outcasts, Corsairs and the Coalition I'd say are unlawful.
BHG, IMG, GMG and Zoners are classed as the same Unaffiliated Lawful.
I'd think to class the Colonials and Order in the same way, but the table has them as Unaffiliated Lawful and Unlawful respectively.
Nomad factions are technically against the law, more 'hated by lawfuls' (and most unlawfuls) than anything. Unlawful as they need to be classed as one of them.
RoS are rather strange. Their current goal is lawful and they only fight unlawfuls, and yet the table has them as unlawful. Possibly due to their past alliance with the Outcasts, may just need updating.
For the other player factions, I'd say MM~ and IND are both semi-lawful, working for both sides of the law and the former shooting both sides too.
That leaves the 'obvious' semi-lawfuls as Junkers, Gallic Junkers, Hogosha and Unione Corse.
Oh, and the Privateers are semi-lawful to me, their past with Bretonia's acceptance of them reflects this.
Well like the last 80% of my post went on to say, I've got my own views on most of it. The table was made by the devs as far as I know so, not counting any changes that may have been made since then, it'd be a good basing point.
Really, the Wiki is meaningless. The IDs page you are referring to does not even list semi-lawful (it lists Junkers as a Guild ID). Then there are the system-specific pages that list the local factions by affiliation, such as Tau-29 that shows Zoners as semi-lawful and doesn't list Council at all. Meanwhile the faction pages use different naming (eg "quasi-legal" for junkers) or are contradictory (NPC Zoners are "independent"). Really, ignore the wiki. It's why I'm looking for an authoritative list.
A lot of corporations do under the table dealings with unlawfuls. However this is true of nearly every corporation so I suppose its less important than the 'main' ones. OS&C has more dealings with unlawful groups than most corporations however.
Not to mention their 'strength' is the ability to blackmail any senator or politician in Sirius. But it really comes down to what do you define as quasi-lawful. OS&C doesn't participate in unlawful acts itself, it just funds groups that do.
It honestly depends on how you're trying to organize them I guess.
If you wanna go from an RP perspective then think of it like this.
Gonna use the SCRA| as an example of inRP semi-lawful here:
The Coalition government sees itself as exactly that, a legitimate government, and the SCRA see themselves as a legitimate lawful military force. HOWEVER, the House Governments and pretty much everyone outside of Omega 52 see the SCRA and the Coalition government as nothing more than terrorists.