I don't know, what you mean with "shotokan has 5 levels" and so on.
But you can look at "using martial arts" as one weapon (unarmed weapon). All your learned martial arts are mixing to one unique fighting style of your character, boni are stacking, you can deceide which damage you use and so on. For example, if you have shotokan an muay thai on base degree, you get all the boni (which would be +5 attack (unarmed) from shotokan), but could use the damage of muay thai (20 + doubled strength bonus).
If you had Malla-Yuddha and Sambo on advanced, you would get +20 block (unarmed) (+10 for malla-yuddha and +10 for sambo), also you wouldn't get damaged from unarmed blocking (advantages of malla-yuddha), you would half the penalties for take down, disarm, trapping and area attacks (advantages from sambo).
To the katana: A weapon wouldn't usually get the boni from the martial arts, because they are only for unarmed fighting. So, if a character is wielding a dagger and has shotokan, he wouldn't get the attack bonus from shotokan. For this, you would have different ability scores
But there is a exception: If a weapon is associated, the weapon get the bonus from the martial arts. Now, you have asked for shotokan, katana and muay thai. The katana is associated with shotokan, so the user gets the shotokan-bonus, if he wields a katana. Muay thai doesn't have a bonus, so unarmed (shotokan + muaythai) and the katana should usually have they same value.
Here are a example for my new character: She is trained in Shotokan, all weapons associated to shotokan and the wakazashi. Therefore, with shotokan and all associated weapons, she gets the +5 attack bonus from shotokan, but the wakazashi wouldn't get this bonus. Therefore, here attack score with the wakazashi would be 5 points below all her other attack methods.
But: The attack/defense bonus from martial arts are like inniate class boni to attack/defense and therefore have a limit at +50. My character gets per level +5 to attack. At level 9 her "inniate class" bonus for shotokan (and associated weapons) would be at the maximum (+5 per level * 9 leves + 5 for shotokan), and at level 10 the bonus for the wakazashi would be at the maximum. (If I doesn't take one or two additional degrees in shotokan XD).
And thanks for this questions, because of this questions I have re-read the weapons-part for martial arts in the DE. I had totally forgotten the rule for associated weapon and the attack/defense bonus XD