agree with Haggis, lots of instant small consequences.
talking back - to your room, because your sister and I don't want to listen to that way of speaking, you can rejoin us when you can speak properly.
ask to do something and they won't do it? Fine, I will remove one toy from your room, for every time I ask you to do it. (chose a toy they care about, return it the next time they do something first time of asking). Or frog march to the task and do it with them as if they are a puppet. I accompany this with a stream of silly voices (Oh no! dd won't pick up her shoes and put them on the rack, quick quick lets get the shoes before they run away - I put my hands under theirs and we double march to shoes and I put them in her hands and make her put them on the shelf) Then, usually they have stopped being cross by now, I turn them round and say in a serious voice - next time do it yourself please.
Shouting and screaming? we don't like that, it hurts our ears, so you need to go out of the room when you do that. Put her out of the room you are in and shut the door. Older child, send them to their room.
If they won't go to their room, I'm afraid I pick them up and take them, usually in fireman's hold and I will tickle them on the way, which changes the mood anyway.
Change the consequences to funny ones - I can't stand that noise, so I am going to turn into the TICKLE MONSTER if you make that horrible screaming noise again, then chase them round tickling them.
Don't forget the basics, are they hungry, have they had exercise (kick them out into the garden for a bit) have they had your attention, are they over tired.
Go on strike - mummy I am hungry - hmm, well mummy is on strike, until you can be nice to me/speak politely.
At mealtimes, rude behaviour means you remove the plate and wait, when they apologise and speak politely return the plate.