Fed up means one is tired of something that is really a bother too long and they not getting any where with it. it can be food, life just about anything.
I guess if you're fed up you can't take any more... food (or anything else)... you've had enough. All those phrases seem to mean the same thing, and all seem vaguely foody; I'd guess that's where they came from.
Say u get chicken every night for dinner then one day u are going to say im fed up of chicken. its the same with everything else in life. u can be fed up of a bad relationship. Fed up of the cold here in London. things like those