They're all technically correct, but the normal collocation is 'have breakfast'. I'm sure that your English coursebook taught you the phrase 'have breakfast', and that is what you will hear native speakers say most of time.

We generally use 'have' with all meals e.g. "When should we have lunch?" or "Where did you have dinner last night?".

'Eat breakfast' is OK, but it's less common.

You'll never hear anyone say 'take breakfast' - it is very outdated. You can forget about 'take' in this context.