I have a 20 month old, and am having many of the same issues as you are having. So I really feel for you!
I suggest a lot of humor. Do anything you can to invite cooperation from her. And, if you are "asking" her to put her toys away, and she says no, I feel like you need to respect her answer. So, if you really want her to do something, don't ask. Phrase it in a way like "There are toys all over the floor! We should pick them up together. How fast can we do it?"
She is starting to exert her independence, which is a GOOD thing, right? We all want to have independent, smart children who have the ability to stand up for themselves and say no.
I don't believe in punitive discipline, like time outs. I have tried sitting on the couch for a cuddle when my daughters go over board. I have tried leaving them alone to scream and get their anger out. Mostly I acknowledge how they are feeling "you are really angry that he took a toy from you", and try to give them the tools as to how to deal with that. Even if they hit, I try and talk like that too, with a firm "You may be angry but we do not hit". As you see, there are many "I try..." because each tactic doesn't always work in every situation!
So, all that stuff said, I have found "Positive Discipline" to be the most helpful book for me in teaching my kids at this particular age. It talks about using kind and firm words and actions. Also, "Playful Parenting" and "How to Talk so your kids will listen and how to listen so your kids will talk". All these books suggest many wonderful things that help you teach your child all the important things you want her to learn.
GOOD LUCK!!!! She sounds like a frisky little girl!