Are all of these correct?
Please get your parents to come tonight.
Please have your parents to come tonight.
Please ask your parents to come tonight.
And which is most suitable to sound more pressing and urge that person?
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If you want to strengthen the request,then encourage is a perfectly acceptable word.
Please encourage your parents to come tonight.
While there appears to be a consensus that get your parents to is "correct", I cannot avoid the feeling that it is at least inelegant. Although you might say it in conversation, I would avoid the expression in writing.
The most formal and appropriate to a wide range of situations is the third in the list. This would be appropriate for a teacher to say to a student for example.
Number one is correct but quite colloquial (as are many phrases with "get"). More likely to be used between peers: Get Mark to call me when he's home.
The second phrase is grammatically incorrect. It should be: Please have your parents come tonight. But it is unlikely to be used in this context as the person carrying the message (the child/student) doesn't have the authority to do so, or it is simply inappropriate. In a business setting, leaving a message with a sectretary "please have Mr. X call me as soon as possible" is appropriate and common.