I'm a bit confused on what your questions are.
First of all, HI is not a strong acid. The only strong acids are the ones you've had to memorize (I believe there are 6). Every other acid is weak.
Well, no, Ka and Kb wouldn't help determine if a species is an acid or base. Actually, it will, but you'll just look at the subscript a and b rather than the number. Because a base wouldn't have a Ka, and vice versa.
But you can see how strong the acids or bases are from the K constants. They're the [products]/[reactants], right? So, look at it from a math perspective. If the K constant is a large number, are there more products than reactants. If the K constant is a tiny number with a large negative exponent, there are more reactants than products at equilibrium.
Also, do you know the three ways to see if a species is an acid or a base? There is the Bronsted-Lowry and the Arrhenius theories (these talk about the H+. Acids are the ones that give the other species a hydrogen, also called a proton), and Lewis structure (this one talks about the electrons rather than protons. An acid accepts a pair of electrons from the base.)