The Anvil Strike Force is the Space Marine version of an armored company. It allows you to field an army composed predominantly (or completely) of tanks. Space Marine players aren't as much of tread-heads as Astra Militarum players, and Space Marine tanks don't quite bring the firepower of Astra Militarum tanks, so this probably won't be the strongest or most common army. Even so, it's fun to have the option.
The Anvil Strike Force comes with two Command Benefits. First is Master of Mechanized Warfare, which allows you to choose a vehicle to be your Warlord. If you do, they get the Big Guns Never Tire Warlord Trait. At the end of your shooting phase, your Warlord or another vehicle within 24" can fire its weapons a second time. Compared to most Warlord Traits, this is actually really strong as it essentially gives you another tanks worth of firepower in your army.
Armor of Contempt allows all vehicles in the army to ignore Crew Shaken and Crew Stunned damage results, though they still lose hull points from any damaging hits. This is very useful because it allows your tanks to maintain their fire even when they take damaging hits. It removes "stun-locking" as a viable method of countering your tanks.
The Anvil Strike Force is composed of 1-2 Core choices, 1+ Auxiliary choices, and 0-2 Command choices. The other major limitation is that all squads in the army have to have a transport included for them. This doesn't say dedicated transport, so I would say that you can use Land Raiders to transport units without a dedicated transport. The Core choices are either an Armored Task Force or Land Raider Spearhead, each of which have specific advantages. The Armored Task Force allows you to take a lot more firepower, as it is composed of Predators, Vindicators, and Whirlwinds. These are cheaper tanks with good weight of fire at a budget price but they lack durability. The Armored Strike Force already ignores Shaken and Stunned results when within 6" of a Techmarine, so this is completely superseded by Armor of Contempt. It does have the benefit that it contains Techmarines with a bonus to their repair rolls. The Land Raider Spearhead sacrifices some firepower for a lot more durability.
The Command choices are very simple. You can either take one Predator, Vindicator, or Land Raider, or a Techmarine in a Rhino or Razorback. The option to take a tank by itself is handy in case you want a tank that's not part of one of your Formations. For example, you might take an Armored Task Force as your Core but want to take one Land Raider to use as a durable Warlord. This allows you to do so without taking a Land Raider Spearhead.
Your Auxiliary choices include the obvious Anti-Air Defense Force and Suppression Force, which give you access to Stalkers, Hunters, and more Whirlwinds. You can also take Mechanised Infantry choices, which include essentially all Space Marine Infantry units. They just need to have access to a transport in the army in order to fulfill the limitations of the Anvil Strike Force. You can also include a Storm Wing or Raptor Wing Formation to give yourself some air power. You can also take individual units of Land Speeders, Techmarines, Thunderfire Cannons, and any type of Dreadnought to round out your force. Finally, if you play Ultramarines, you can have Sergeant Chronus take command of any tank in the army (he'd make a particularly good Warlord).
Overall, I think the Anvil Strike Force would be fun to play and would be great for certain narrative games where you want to represent a convoy or an armored assault. However, I think they missed out on some rules that would make it more interesting. The base rules of the Strike Force are useful but pretty lackluster. Personally, I would like to see Chapter Tactics apply to the vehicles in the Strike Force. This would require some modification to Chapter Tactics to make it work, but right now, only the Iron Hands Tactics really benefit the Strike Force. For example, I would allow tanks in an Ultramarines Anvil Strike Force to benefit from Combat Doctrines, re-rolling 1's to hit from the Tactical Doctrine and all missed to hit rolls from the Devastator Doctrine. I would also grant the Strike Force access to another Devastator Doctrine. Imperial Fist tanks could re-roll 1's when firing heavy bolters and Predators would gain Tank Hunter. Raven Guard tanks could have Shrouded for the first game turn, while White Scar vehicles could Scout (though not Outflank; I think outflanking Vindicators could be a bit too strong). I'm not sure what to do for Salamanders; perhaps all of the vehicles could get Reinforced Ceramite.