The versions with food, meal, cake, and sandwich all sound fine to me. The one with dish sounds peculiar – unless you are talking to a chef who is preparing a dish:
Please finish your dish, so I can use the stove.
This is one of those ELL questions that makes me marvel at our confusing language. Grammatically and syntactically, there's nothing wrong with, "Please finish your dish." And it's not like dish is such an unusual word; it's used often enough to refer to the main course of a meal.
I suppose we can make it sound a less strange by adding some more context:
I don't care if you eat your carrots and peas, but please at least finish your main dish. Shrimp is too expensive to just throw that all away, and it won't keep overnight.