Hi Aunt Sand,
It definitely sounds like you're at your wits end, I'm sorry to hear it.
From your story I'm hearing that these kids are craving attention. I understand there might be some special needs involved, too - but most often making adjustments for these is easier than one might think. Allow me to discuss a few possible options.
If the kids are being ungrateful it's most likely because they've been handed things instead of working for them. I am not saying put the kids to work with chores, but... Put the kids to work with chores! Here's the trick tho: make the chores highly rewarding. They want 3 different meals at once. Fine. Get in the kitchen and start learning how to cook! Side-by-side, you can spend time with them as they learn a new skill AND get what they want. They'll probably object at first, but hey, if they wanna eat, they'll either get on the bus and start preparing their own insane varieties of meals, or they'll eat whatever you make by default.
If they want those expensive experiences/things, they can purchase those things themselves. I believe it's still legal (and often mutually beneficial) to pay nieces and nephews for doing chores around the house. Well placed and managed, a little bribery can go a long way. And giving kids an opportunity to complete tasks builds their self-esteem - I would imagine that with so little attention at home, this could only be a good thing.
Allow them to use their devices at their leisure, but only during certain periods of time. Resort to hiding them if you must, at first, for brief intervals of, say, silly string fights. Have you ever handed a kid a bottle of silly string and NOT seen fun break out? Plan an impromptu activity like this that will take them out of their I'm too cool for school attitude - take them by surprise! And while they're on their devices, take time for yourself to read a book. Pretty soon, if you all sit near each other during this time, they'll take an interest in what you're doing. Or you could even do the tried and true method of playing the games they're playing on their devices. They'll either love it and play with you happily, or they''ll see that your interest makes the stuff uncool and look for something else to do.
But before any of these ideas will be useful, it sounds to me like you might want to clearly define your boundaries and expectations with the kids. This is your home, your life. Your experience has given you something valuable to share, and you're happy to share, but what kind of example would you be setting for them if you shared with people who disrespected you and treated you badly (no matter how old they are)? It's ok for them to know that life is one way with mom and dad, and things are different with Aunt Sand. Again, they will probably object at first, but if you stand your ground, have confidence in what you have to offer, keep your word, and practice consistency, the kids who need the most attention generally come around the quickest and appreciate it the most in the long run.
My best piece of advice, however, is: don't self-identify as a ogre! Detach yourself from the sting of their outbursts, remember: they're just kids. Zen yourself out when the going gets tough and allow yourself to respond to hard attitudes with a soft touch. Behind every behavior is an emotion and/or a need: address the emotion and meet the need.
I hope this helps.
Stand in your truth, Aunt Sand, and you'll reap the benefits!
Good luck!