Okay, awesome. So basically, from what I am reading, cardinals obviously can fly and like most summons, can telepathically communicate with their summoner. That being said, they have pretty aggressive bonuses. One being from what their true affinity is, and the next depending on whether or not they are in the weather that coincides with their affinity (are these stackable?). That is the base of what they may do. Now to break down each one.
Aphrodite, the queen of the cardinals, is able to be summoned normally, but once entering battle, envelopes in flames in which she would now have about regal armor plating her "strategically", as you put it. I like that. She follows this up by the flames bursting forward in B-rank fashion. This goes up to mid range and also aesthetically lights her feathers on fire (as far as I am aware) but obviously not harming her. Her two affinities, which are wind and fire, she can perform up to A rank, which is pretty solid considering the boost(s). Other than that, she is described as egotistical and stern, having her summoner prove they deserve to battle at her side. However, this doesn't get in the way of her battle intelligence. Love it.
Keleano: Oh lord... Aphrodite's younger sister... I wonder. Anyway. Similar attributes as her sister but a water/lighting affinity, able to specifically fit two riders on her back, and slightly smaller than her older sister. The stream she shoots is B rank as opposed to her sister's A rank as well as water as opposed to her sister's fire. This water leaves her wings wet, creating a water source for her to perform water-based techniques. Besides that, she is arrogant, thinking she can take on any summon. Even those clearly more powerful than her, but will stick by her summoner and is still very battle-hardened herself.
Mother Earth! A small, old bird who sits on the summoner's shoulder. She has a husband who is equally as small and old. Her gig is genjutsu in which she can perform any genjutsu the user knows up to A-rank. This is perform through a bird call of sorts. A simple summon but effective.
Kurt Travis. A taijutsu master and small enough to sit on the summoner's shoulder, much like Mother Earth, Kurt's main gig is to boost the user's taijutsu by +10. This is done by him channeling his own chakra into the user and enhancing their physical blows via his chakra. Again, simple but effective!
This is my breakdown of the contract as well as all of the current summons.