Can you help me think up creative solutions for what may be the pickiest eaters ever to live?

My stepkids are finicky eaters, they always have been. The problem is, like most picky kids, the stuff that they dislike is everything that is good for them. They live on junk.
My parents were always from the school of thought that you should put a plate in front of them of whatever you’re eating, and if they don’t eat it.. fine. Eventually they’ll get hungry enough that they’ll try anything. Well, that isn’t even an option. The last time my husband and I withheld junk food from them, we were accused of neglect in family court. The accusations didn’t hold, of course, but you can imagine that when I say we have to do this in baby-steps, I mean baby-steps.
I really have not ever met anyone more particular than these kids. Of course, they are independently picky, as well. One eats ketchup, one doesn’t. One eats hamburgers, one doesn’t. Etc etc. They don’t eat soup, beef, pork, and they are really particular about chicken. Neither of them eat any vegetables. One of them eats fruit, the other won’t touch it. They are only interested in heavily processed foods, and they will literally just refuse to eat anything if there is something on their plate that they don’t like.
They are overweight and they have to be nutritionally deficient, but I have no idea how to change that without fear that it will blow up in my face.

Are there any creative tricks for getting some nutritional foods into their diet, even if it is alongside the junk that they eat now? I find myself wracked with guilt over feeding them the stuff that they like, but I also feel like I’ve been backed into a corner. Help?