Bibliii
Ka = the equilibirum constant of an acid dissociation reaction eg for the equilibrium system HCOOH + H2O <-> HCOO- + H3O+, Ka = [H3O+][HCOO-] / [HCOOH] (remember you exclude water for aqueous equilibria since its concentration change is negligible)
pKa = pH above which half of all acid molecules are deprotonated. Given by -log10(Ka), so higher pKa = weaker acid. If you inspect a titration curve, they're the half way points between equivalence points. They're really flat since when pH = pKa, an acid buffer system is most resistant to change according to the Henderson-Hasselbach equation (I don't know to what extent banana benders need to know this, I only learned Ka in uni chem in Victoria). You can memorise the property of pKa by the fact that when pH is above pKa, the equilibrium system is deficient in H+. According to Le Chat's principle, the system will want to partially oppose that, which it will by having your acid donate its proton.
Kb = the equilibrium constant of a base ionisation reaction eg the Kb for NH3 + H2O <--> NH4+ + OH-, Kb = [OH-][NH4+] / [NH3]. Kb and Ka can be generalised as [ionised species] / [unionised species]
pKb = the pH above which a base will be protonated. Similar story with pKa, when pH is above pKb, the system knows there's not enough H+. To compensate, you'll want less OH- in solution, forcing the base ionisation reaction to proceed in reverse
H3O+ = the protonated form of water, ie its conjugate acid. Abundant in acidic conditions since the acid has donated its H+ to the solvent molecule (H2O).
OH- = the deprotonated form of water ie its conjugate base. Abundant in basic conditions since the base has stolen H+s from H2O.
One small correction to jinx's excellent response, technically strong acids also have Ka and pKa values despite the fact that strong acid ionisation is pretty irreversible. For example, we are required to know in uni that pKa of HCl is -5 for purposes of comparing leaving group strength in organic reactions. Ditto for strong bases with regards to Kb and pKb
I don't know how QCE structures their data tests so someone else can help with that