I think it's pretty strange the different houses don't have signature attacks, considering they are all marital houses and many have valyrian steel swords. GRRM is usually pretty accurate about things historically but think he may have overlooked different moves and fighting styles.
The Starks generally use greatswords and would probably use honourable tactics and great sweeping motions with their blades, making clear their intentions in a fight and not misleading the opponent.
The Boltons would specialise in blazing speed, utilising razor sharp knives in battle wielded with both hands to slash at an alarming rate. They would trick opponents, exploit openings, inflict bleed damage in conjuction with acrobatics and light armour types like chain mail and leather.
Heirs of House Lannister could use a battlecry that mimics the roar of the Lion - their sigil - to double attack power, speed and ferocity but at the cost of stamina (Hear me Roar)
Tyrells use horses in Battle and lances to make up for their slight builds and practice against three men in order to bring their skills up to the level of the other great houses.
Greyjoys are thought to be great archers and also use impenetrable iron armor with helmets shaped like krakens to inflict fear against opponents. They never back down from a fight and have massive defense, endurance and are fast learners when it comes to improvising in a fight. Their massive plethora of weapons is axes, swords and spears but they prefer axes which most are very deadly with.
House Martell use throwing spears but also regular spears that they coat in poison (Oberyn Martell - aCoK) which is thickened basilisk venom for a quick or slow death depending on the quantity used. They use a darting motion like the snakes of Dorne with spear jabs and they use metal shields that while heavier than oak sheilds can be used to reflect the sun at opponebts in a fight. They are also proficient swordsmen but are quite rash. Their blades include longswords and scimitars.
Baratheons use massive weapons like Hammers with deadly effect in conjuction with exquisite green amd gold stag shaped armor. They have huge attack, strength, stamina and endurance and can increase these attributes in allys with a battle cry. Excellent leadership and lightning fast reflexes make a fully armoured baratheon truly a nightmare made real.
Thoughts on other houses?