Honestly I think it's too late for consequences etc - they don't respect you so that isn't likely to magically change their behaviour around, it will just make them combative. That approach can work but I think you need to start it when they are younger.
I'd probably go back to basics with the younger ones - daily routine and consistency just because that's an easy win and will help with a sense of calm in the house in general. Up to age 6, get up at a decent time, everyone dressed, breakfast and go and do something. The 10yo will be fine staying at home for a short time - the teenagers are there in case of emergency. I wouldn't leave them all day but for a short time no problem. They'd get bored being dragged around toddler activities anyway.
For the eldest two just back off a bit and only ask for the basics from them/offer the basics to them - whether or not in your house that usually includes laundry and meals, but no favours, no money other than regular pocket money, no lifts unless longstanding arrangement, etc. Pick battles with 10yo as well. This is about establishing a new routine, not starting a boot camp that you won't be able to keep up long term.
I can ask my 13yo to help with my 3yo and baby - but only when I've kind of primed him to do that. If he was under the impression it was school holidays and he was free to do whatever he wanted and then suddenly I ask him to do favours he will kick off because it seems unfair. That's their teenage lack of perspective, but it's also kind of right in a way - younger siblings are not a teenager's responsibility. So I approached him at the start of the holidays and said look - you have unlimited internet now, (we used to "pay" him in internet time to take the 3yo out) I'm on my own, (in the day) I'm going to need help occasionally. I don't ask often but I do ask him to occupy them sometimes.
So once you are in the swing of a calmer house, approach the 15/16yo, adult to adult style, and problem solve. Include the 10yo in the discussion if you want to. Forget childcare for now - have no assumption of childcare from any of the older ones. But talk about keeping the house running aka household jobs, that's a good place to start - all the kids from 6yo+ can have some kind of job that they do to help out in the house. Get them to come up with a list, or present them with a list that they choose from, or just ask everyone for one job they hate and will be guaranteed never to do and one they don't mind doing. Or just talk about expectations and what they want vs what you want. Just take it out of the moment as in the moment is much too emotionally charged.