All of the responses I've read seem to have good advise. My daughter saw a great individual counselor who comes to the local pediatricians office, and he was great. He was a real expert in how to manage anxiety- which comes out in so many ways.
Be as positive as you can with her any chance you get. At some point, it would be worth explaining to her how important it is to be known as an honest person. My 10 year old was exaggerating a lot last year, and I told the story of the boy who cried wolf to her and her little sister, and we talked about how bad it was that noone believed him. Then I talked about how much easier it is to get what you need in life and have people listen to you and trust you when they KNOW you are an honest person. If you steal, or make up things, or hide things, then when you really need something from someone and need them to hear you, it can take a lot of work for them to believe you. I used their grandpa (who is a respected and humble man) as an example. When people come to him for advise, they believe him. How nice it is that people just naturally believe what he says, because he doesn't have to work hard to convince people of things. My kids get it; how nice that would be to be that person who is trusted, to not have to "prove" yourself trustworthy. I still call my daughter on it when she seems to be exaggerating; sometimes playfully. I don't want her to think she is bad, just that it is bad for her if she is not honest.
I also agree with the responses suggesting there is a possible emotional "eating disorder". I absolutely recommend removing the "bad" food from the house, and being sure to sit down as a family at least one meal a day, and taking time to ask her specifically if she wants more of this or that. For her, eating has become something SHE does for HERSELF ALONE. It may help to remind her it is a community event.
Eating could be a way of isolating herself, comforting herself, doing her own thing, controlling her eating (in a similar way that anorexic's may hoard food)- all of which have a strong emotional component.
Also, sugar is a drug, and some of us CRAVE it until we get it out of our diet. My five year old does all the things you describe in your daughter, yet because she is five, I have chalked it up to her inherited sugar lust. But I DO call her on it when she sneaks, I DO keep sugar out of the house now, and DO talk about good food and the benefits of different foods all the time. She still begs for candy, and I offer something else instead and she just has to deal with it. She knows that every now and then we get ice cream or candy, so she is also learning about patience!
Good luck- she needs to get comfortable with how to handle her emotions now, before puberty brings her new feelings that cause increased anxiety. I highly recommend her own psychologist.