I am used to saying 'have/take your dinner' and 'eat your food'. Is it correct to say 'eat your dinner'?
Is it just a matter of style and preference?
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As stated in the comments above, "take your dinner" sounds a bit outdated. It is probably better to say "eat your dinner."
On another note: PERSONALLY, I have never heard anyone say, "Have your dinner." I have heard things like, "Come have dinner with us," but I have never heard the phrase, "Have your dinner" by itself. I'm not saying it's wrong though.