Eat your dinner

As stated in the comments above, "take your dinner" sounds a bit outdated.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.

If I'm not mistaken "take your dinner" is American English, while "eat your dinner" is British English.

I think it's a matter of style and context of the conversation.
For example when you say "take your dinner" that would make me think you're working late and taking your dinner break

"Eat your dinner" is American English. "Have your dinner" is somewhat anglicized English (i.e. Canadian or British.) "Take your dinner" is not standard in any primarily anglophone country, as far as I know.

Take your dinner is not Standard American English, unless you are saying, “Take your dinner with you.” Take your dinner sounds from Spanish,”Tomaste la cena.”