This is covered on our FAQ, I believe, but minions try to move closer down the Blue/Green axis then, if that won't bring them any closer, down the Red/Yellow axis. You move the minions closest to the objective first. If they're tied for closest, the closest along the Blue/Green axis. And in the rare event they're still tied for closest, the first player decides.
It depends on the mission. The FAQ states for Mission 1 that minions prefer green/blue movement over red/orange. That's essentially east/west if you consider red points north.
In Mission 2 minion movement is more scripted along set paths, but there are situations where moving one minion before another would cause a big traffic jam. I'm not sure how this is resolved, but the FAQ mentions in Mission 3 that if
Spoiler (click to reveal)
is the same distance from two targets the first player can choose which way it moves as long as it moves closer. I assume minion movement issues can be resolved in a similar manner.