Is it the light or the sound from the TV? You could start by reducing that, by covering the screen with a blanket, and add more light-blocking stuff over a few weeks until you don't need the light anymore, or by slowly turning down the volume until it's super quiet/gone.
I don't think staying up late to fall asleep when you have to get up early is a good idea. Have you tried taking Melatonin? It makes you a bit sleepy, so it's easier to fall asleep.
Unfortunately, there's no way to really make your body adjust when you schedule varies that much. I'm a bit confused about your schedule, if you're saying some days you might work overnight? Do you have shifts where there's only a few hours between getting out and going back? In those cases, I would say take a power nap between shifts, then get an appropriate amount of sleep at a reasonable time, considering whenever your next shift is. So if you had an overnight shift followed by an early morning shift, take a little nap (1/2 hr to an hour) in between, have some caffeine, and if the next day is an early shift, get to bed at a time where you can ensure about 10 hrs to make up a bit, but not oversleep.