Is there a manager or somebody above her who you can talk to? Somebody needs to set her straight and confirm whether or not this fridge is communal or solely hers. Then said manager can tell her not to put her shopping in the fridge so nobody else can put their food in, and also that she is not to throw food away that is not hers. She sounds like a real control freak and only a manager can set her staight. She is likely to kick off and still do it but it is better to put her in her place and if she continues then there are grounds for a disciplinary and then if it continues, there are grounds for termination of employment.
I had a similar situation. Where I used to work there were break out rooms on every floor. The floor I was on had a woman who was a real b-word when it came to the fridge. She'd randomly throw other people's food out because she felt that they shouldn't be eating it - not because they were mouldy or whatever.
When confronted by management she said that if school could encourage kids to eat healthily, the company had a moral obligation to ensure people at properly and if they didn't she would. She was got an informal disciplinary.
After that she got really bitchy - she would wait in the kitchen and tell people 'you can't put that in there' rather than taking them out or she'd leave passive aggressive notes on people's desks (she literally told a plus size woman in a note that if she ate unhealthy food she wouldn't be so heinously overweight and a strain on national resources - the woman had a cheese sandwich, a packet of crisps, some yogurt and a small chocolate bar in her lunch box - hardly deep friend and unhealthy). That earned her a formal disciplinary.
Then she decided she would fill every shelf up with her own stuff to stop people using the fridge. Then she got her final warning and she decided she was being discriminated against and tried to take legal action. After a really messy few weeks and her making everyone's life miserable she was fired. She tried to take legal action against that but as far as I know, she hasn't succeeded.
But yeah, the best way is to set these people straight. The company might decide to take away the fridge to resolve conflict, which will be bad for you but at least the cow will also lose out and learn not to be such a b-word.