Do sleep masks work if you are sleeping on a regular nighttime schedule (e.g. 10PM-6AM), but the room is lit?
First, it depends on what kind of sleeper you are. Can you get to sleep and stay asleep with lights flickering? I can't, my husband can.
Also, it depends on what kind of lights are going to be on and off during, and especially, before your sleep shift. Lights that are in the blue spectrum, like TVs, computer screens, tablets, etc are more likely to affect your circadian rhythm and your sleep cycles, this can lead to depression. Daylight at bedtime (or the lack of) can also affect your body's natural production of melatonin, which is the hormone that helps you sleep.
Some people have luck wearing UV protected sunglasses before bed to limit their light exposure. Some use a sleeping mask during their sleep shift (like me). I can't even have an alarm clock in my room because the glowing display will wake me up. It is important to have a good before-bed routine, and try to limit your light exposure during that time. Do not watch your TV/smartphone/computer to put yourself to sleep. Give yourself at least 20 minutes of quiet and low-light reading, Sudoku, or meditating before closing your eyes for sleep. Make sure you get enough daylight during your waking hours, too.
What alarm clock options are available to those who wear a sleeping mask and earplugs to bed?
I find that an iPhone is easily loud enough to wake me when I'm wearing ear plugs, but any alarm that's sufficiently loud & close to your head should do it.