When Carla goes to the bathroom to take a shower tell her to "Take it easy on the soap" because last time she used up the whole bar of soap in one shower.
Made popular by the song of the same name as most popularized by the band called REO Speedwagon in the 1980's era, take on the run means to run away, usually from a bad or uncomfortable situation.
It may also now refer to taking a food order to go, aka running with it.
He suspects that you're cheating, so like a coward instead of confronting the situation you leave town and take it on the run.
I don't have time to sit down and eat. I'll just take it on the run.