You must take 1+ Auxiliary Formations in a Gladius Strike Force in addition to the Battle Demi-Company. Beyond that, these Formations can also be taken individually to supplement your army. This is perhaps the most valuable way to use these, as it allows other Space Marine Chapters, such as Blood Angels, to take some of the newer Space Marine units that aren't included in their codices.
The Anti-Air Defense Force requires a unit of Hunters and a unit of Stalkers, and there have to be at least two Stalkers in the unit. With a minimum cost of 220 points, it's a cheap way to add anti-air defense to your army (hence the name). The Formation special rule is Skyspear Autotargeting, which states that if the Hunter hits a Flyer, the Stalkers get +1 BS when firing against the same target for the rest of the Shooting phase. It's a useful perk if you remember it, but it doesn't add that much. The big advantage of this Formation is that it provides the cheapest way to add anti-air to your Gladius Strike Force, as well as to other Imperial armies that lack affordable anti-air options. For just slightly more than the price of a Stormraven, it gives you a much better chance of downing enemy flyers early on and I suspect it will be a popular Formation throughout the Imperium.
The 1st Company Task Force is one of my favorite Formations, but I really like Sternguard, so I'm biased. The Task Force consists of 3 to 5 Veteran units, including Sternguard, Vanguard, Terminator, and Assault Terminator squads. As special rules, they all receive Fear and Fearless. The big advantage here is Fearless, as you know that these squads are utterly reliable and won't fall back or be pinned when you need them.
In addition, they get Extremis Level Threat, which allows you to nominate one enemy unit at the beginning of the game, giving all members of the Task Force Preferred Enemy against that unit. This is particularly useful if the enemy has a key lynchpin unit, but the units within the Task Force are skilled enough that they shouldn't need it to take out most targets, so don't worry if you need to spread out their killing power. Just pick one of the first units you plan to kill with any member of the Task Force, wipe it out, and move on.
Finally, the Task Force gets Terrifying Proficiency, which is a -2 LD penalty on any enemy unit within 12" of 3 or more units from the Task Force. This is surprisingly easy to do between combat squads and Dedicated Transports (which count as far as anyone that I've talked to is concerned). While the negative LD aura makes the Veterans much more likely to break their targets, perhaps it's best use is in conjunction with a Telepathy psyker. The potential combos here are both many and devastating. If you're planning on taking more than a single squad of Veterans, this Formation is worth very serious consideration.
The Strike Force Ultra is the Formation for players that love Terminators. It consists of a Captain in Terminator armor (potentially Lysander), 2 Terminator squads, 2 Terminator Assault squads, a Venerable Dreadnought, a Stormraven, and a Land Raider Crusader. That's a big investment, but it comes with a lot of special rules. Ultra Strike requires that the whole Formation starts in reserve, but you get to roll for units within the Formation to arrive Turn 1, which is pretty big, though it will require a way to re-roll Reserve rolls for reliability. Fury of the Storm allows Terminator squads to fire an extra shot with each of their weapons when they arrive from deep strike, while Force of a Thunderbolt gives Assault Terminators an extra attack the first time that they disembark from their transport.
Obviously, Strike Force Ultra is designed for the Terminator squads to deep strike while the Terminator Assault squads and Venerable Dreadnought ride in the Land Raider Crusader and Stormraven. It makes all of the Terminator squads significantly harder hitting against the first target they engage each battle, and they should be able to engage quickly thanks to the ability to arrive Turn 1. The downside to this Formation is the expense, but I really think it gives Terminators the killing power they need to earn their place on the table. Combined with the drop in cost of Terminators in this Codex, I suspect this Formation will be pretty powerful for its points. I hope to try it out once I get more Terminators painted.