i have found a work around solution for now that works but isnt really ideal, especially if you use airdroid in more then one place, i dont often use it outside of work so for me its ok.
firstly i did notice the 4 airdroid process running and like you killing them all did nothing, and ive tried using a tasker plugin to execute shell commands too but nothing worked, my guess is that there must be a file or something that gets created or written too that tells android to launch the program again should it be force exited, but without developer insight or knowledge of android above mine i dont know for sure.
so anyway my work around solution is this, use tasker's built in app kill to kill airdroid and then a few seconds later i use a plugin called "Secure Settings" to full on disable the app, which basically keeps all of the apps data in place but hides the app from the system so it thinks its not there and cant run it, so obviously the app never opens again and it works too no data is lost ive never had any hiccups with the app after doing it etc. the downside is that the app is disabled until you trigger the tasker thing again so you cant open it manually if you want, to get round this i created a tasker icon thingy that reenables it if i click it
it would be alot easier if it was just a simple kill and move on case but this works for now
