Here is an idea I've been kicking around for a while. I feel like since I've got the Carrier orbitting Earth and it's kind of an all-inclusive "that's not earth tech" type ship, because it is a flying piece of ALIEN tech itself. I've been holding off so I could get a better gauge of how people are settling in and work, since I honestly had no idea what 90% of your characters did and I kind of still don't.
Either way, after this massive invasion, I feel like it's a really good time to push forward or at least propose this plan of action.
ALIENS; With some discussion with Nick (forthcoming), I'm hoping to apprehend Tora and take her back to The Carrier (not the Helicarrier) orbitting Earth. Due to the massive invasion of Frost Giants, I was hoping that I could have SWORD agents visit various aliens on the surface to ask them 1) how their stay is, 2) their business on the planet.
Superman; This will be discussed with Nick/SHIELD because aliens ARE SWORD's jurisdiction, but because he is an avenger, I'm assuming SHIELD will want to take care of this. We're proposing that there is a liaison between the two (at the moment we're going with Bobbi/Mockingbird).
Scott Free & Barda; He may be offered a job and more heavily questioned about his relations to the woman who wrecked a part of the Carrier, aka Big Barda.
General Zod; Previously set free, will also be getting a check-up visit to see how he's doing. At this time, SWORD may also contact SHIELD to let them know there is another Kryptonian. Whether or not they want to share this with Kal is up to them. Depending on whether this will interfere with Bill's plans or not.
Genis-Vell; Will get a short visit from Midnighter or Apollo or both. This is up to you Brett. I don't want to force anything.
Hulkling; I'm assuming he'll be overlooked for being a mutant since his mom's been on Earth before SWORD was created and in deep hiding.
Tora; Already will end up in SWORD custody as they try to sort her stuff out.
Miss Martian; She won't get a visit. I'm presuming her uncle's already a member of SWORD and she's been on the radar since her arrival.
Ms. Marvel; I'm not sure how this works, but I think Meesha mentioned she's got some Kree in her.
Kara & Conner; Get a friendly neighborhood visit, possibly with Lois involved because she'd want to chaperone to make sure they're not getting bullied?
GREEN LANTERN CORPS; I feel like since they are operating in Earth's airspace whether active or not, they should be contacted by SWORD to at least try to coordinate/work together?
ASGARDIANS; I'm not sure what these are classified as. If anyone would like to enlighten me, that's cool.
P.S. Please let me know if I've forgotten anyone/anything. <3