Regarding the "priority" of Olimar's upair...
Originally, my testing seemed to conclude that attacks that clash with pikmin based attacks will not clash more than once, but I found later that this clearly could not be the case- as I've seen Olimar's upair continually clash with Kirby's down air on rare occasions.
This can only mean that Pikmin- that is, possibly the pikmin in ALL of Olimar's pikmin based attacks, (excluding fsmash, and conclusively including upair) are to be considered SPECIAL attacks. Let me explain.
When two grounded attacks clash with one another one will clash cancel or they'll both be canceled- a very common example being two characters' jabs against each other where they both come out on the same frame.
When a special attack clashes with another attack the particular hitbox that collided will follow normal clashing properties- that is, it will either clash cancel or cancel the colliding attack. What's different about special attacks, though, is that the special attack as a whole won't automatically be canceled. Ex. A jab combo won't continue if it clash cancels whereas... Meta Knight's tornado will. Olimar's upair follows the same properties... yes, Olimar is flinging a tornado above his head every time he does an upair... a tornado without the vulnerable spot at the top. :D
What I DON'T know is WHY Olimar's upair will cancel out SOME multhit attacks like Fox's dair, but won't beat out others like Kirby's. It may be because the single hits of Kirby's dair do more damage (I think), even though Fox' seems to come out more rapidly. I don't really have the means to test this and found out the answer, though.