Stark is great at military challenges and pretty good at power, but is generally quite rubbish at Intrigue - the Catelyns are pretty much your only good in-house intrigue defense, and Roose Bolton is probably the only good intrigue offense. Stark is also the best anti-control house, and they have lots of cards that prevent all sorts of nasty effects on your characters. Stark has, unlike some other houses, a lot of versatile deck building options that have different strengths and weaknesses (unlike Lany which is pretty much only kneel)
Stark is also the only faction that can use the Siege of Winterfell Agenda, which gives you power from winning miltiary challenges, but stops you from getting power through other sources
The Blackfish. AKA Mr. Draw Engine. He's Stark's best and most reliable in-hosue draw, has renown, and when he's got 3 or more power on him all Tullys attack without kneeling, which is huge.
Guard at Riverrun: Good extra draw for when you dont' lose military challenges - which you shouldn't, because you're stark.
Catelyn Stark (Core): Good anti-intruge/power defender, but does tend to get stealthed/milked/killed.
Catelyn Stark (Lords of Winter):Great for springing on your opponent when he thinks he's got the challenge in the bag. Can't be stealthed out as well.
Eddard Stark (King's Landing): Good generic protection for your Blackfish, your Robb, and himself from pretty much any sort of card. Also gives card draw
Sansa (King's Landing): Because you need intrigue, and because she can potentially be a Strength 4/noble crest/renown character when there's nothing in shadows
Brienne of Tarth (Princes of the Sun): See above.
Robb Stark (Lords of Winter): Greatif you're playing a trait deck: e.g. Bolton, Tully or Direwolf. Can also be a good strength buffer in general.
To be a Wolf: The best search in the game with very little.
Crown of Winter: Almost always finds it's way onto The Blackfish or King's Landing Ned rather than on Robb's head: Great anti-control card which gives selective immunity to your opponent's events/character abilities, but allows you to retain . Also makes it Winter, which goes well with Robb.
Bound by Duty: Allows a character to defend again, and again, and again, and again. Very handy, particularly in a melee game. Probably best played on the Blackfish, because he's the one who benefits the most from getting power put on him.
Endless Endurance: A Repeatble +2 STR surprise card, which returns to your hand every time you win a miltiary challenge by 4 or more strength. Yeah....
Frozen Solid: Very versatile location/attachment control.
Shaggydog (lrds of winter): Reduces your opponents' strength by 2 for EACH direwolf you haveand can actually help you win intrigue challenges. Bonus for standing every time the attached character wins a challenge.
Frozen Outpost: Allows a defending character to stand AND gives a Strength Buff.
Frozen Moat: Blanks an attacking character out. Very useful against the Fox's Teeth, Arianne Martell, Beric etc.
Stark has some interesting builds.
Siege of Winterfell
One of the more common builds out there, but it is VERY VERY one dimensional. You will not win if you don't win military, period, and your opponent can easily play around it to stop you from winning. You'd want to include more Renown characters in the deck to help you win the game slightly faster. The only real autoinclude is:
Storm of Swords; Plot that gives you an extra military challenge.
Probably the most hilarious decktype in the game: Hordes of direwolves chomping on your opponents' characters and reducing strengths to zero. It is very similar in many respects to Targ burn. Often run with Siege of Winterfell. Relies on :
Wolfswood: Gives Direwolves Stealth.
Grey Wind (Lords of Winter): With the number of strength reducers you'll have, pretty much all your opponents' characters will be at strength 1/2....
Feral Pack: Deadly is fun. It's even mroe fun when you're the only player who has deadly and defending against you is practically suicide.
Threat from the North: Pretty much guarantees your opponent won't be able to attack you this round without losing horrendous amounts of characters through your direwolf kneeling
Tully decks rely on using the Tully trait to the full. This means Strength buffs from Hoster and Robb, and getting your characters to attack without kneeling. This deck is particularly effective against Targ Burn, because of its reliance of strength buffs from Robb and Hoster Tully.
Blackfish: I mentioned him above. i'll mention him again. He is amazing in a Tully deck once he gets to 3 power because you'll never kneel to attack again.
Knight of the Red Fork: Yes, he kneels out all your non-Tully Cards. He's also cost 1, and with Hoster and Robb, is strength 6.
Edmure's Host: Because when you're running this many tullys, these are pretty much coming into play for free. And Free Strength 9 armies with the war crest that don't kneel to attack are nothing to laugh at.
Trident Reinforcements: To recover from Valar Morghulises
Riverrun Messneger: Proper intrigue defence, when it's strength 5
Bolton relies on getting lots and lots of cheap characters with high strength itno play, and stealing your opponents' characters
Roose Bolton: (Not yet released): For if and when your opponent has stolen your Boltons.
Abandoned Fort: For grabbing Rogue Boltons back into your hand. Also combos with imposter or devious intentions to allow you to return characters to your opponent's hand. Red viper/Beric, I'm looking at you!
Reek: Good for stealing a character with loads of power on it/with a nasty ability
Devious Intentions: Good for stealing a character, for forcing your opponent to kill off a high-value character, or just to give thme the house bolton trait so you can send them back up into your opponents' hand
Weeping Water: For getting the imposters/devious intentions back form the discard pile
Relies on just chopping your way through key opponent characters and winning through brute force. Probably one of the least subtle decks out there. This might not be the most effective of decks, because it doesn't actually have a realy way of winning. It's just good at stopping your opponent from winning and at annoying the hell out of your opponent.
Bear Island: Easiest Repeatable kill in the game. Completely worthless against a Stark deck though.
Robb Stark (Core): Kill ANYONE after winning a military challenge.
Ice: Surprisingly good deterrent to someone actually defendingg a challenge.
Icy Catapult: Goes on a refugee or other claim soak. When it dies, you get to kill someone!
Routing the Charge: Works very well with surprise Catelyn/Endless Endurance. also deters your opponent from attacking you. Hilarious with Frozen Moat against Beric or the Red Viper