Short Stack/WMG

The video for Ladies & Gentlemen is a near-death hallucination.
In the ending, the girl is seen being defibrillated. In the beginning, however, she seems to be OK. Following this logic, it's possible that something happened and the entire video is her hallucination.

The Bat Country-verse has been taken over by aliens, and the band are part of a resistance movement trying to combat them.
I'm working entirely off the "Planets" video and the trailer for This Is Bat Country, FTR.

Humanoid aliens came to Earth and lived among the people, claiming they only wanted to live in peace. However, these aliens secretly began to take over Earth by getting close to people in authority and taking control of them. A group of people who disliked the aliens formed a resistance movement after they discovered that their planet was about to be taken over. The aliens took over openly but declared that they weren't going to harm humanity or fuck the planet over. However, the resistance movement, under the name 'Bat Country', has been engaging in guerilla tactics, driving the aliens to open warfare.

Now, the video for "Planets".

The pale alien was allied with the other aliens, but it decided to defect. However, its defection was discovered by its superiors, and it had to flee. The alien hides in the masquerade ball, where it was meant to be picked up by the resistance, among neutral and enemy aliens and humans, hoping that the resistance will find it before the enemy does. The band and the dark-haired girl were meant to retrieve the pale alien, but the dark-haired girl is captured by the aliens. They torture her to try to make her give up the location of the pale alien (the dried blood on her cheek in the beginning of the vid) but she stays quiet. They then give her to the blonde alien, who manages to get the location. Blonde alien dispatches her minions to the ball, and they capture Shaun and the pale alien just as the pair are about to escape.

Now, the trailer.

Andy and Bradie manage to escape and contact the resistance- who respond by attacking and successfully taking over a strategically important city. From there, they prepare to rescue Shaun, the alien and the dark-haired girl, which may or may not happen in the video for "We Dance To A Different Disco, Honey".
 * CONFIRMED by the aforementioned video (except for them rescuing the dark-haired girl, and taking over the city wasn't mentioned either).