Your friend asks you if you want to go to their vacation house in Hawaii with them, and you have transportation, money, your phone and its charger. All you don't have is your parent's OK. What do you do, especially if they're extra strict?
Prove to them that you are mature enough. This may be included as babysitting for your sisters and other families, dog-walking, lawn mowing or snowblowing, not for the money, just to prove that you can take care of yourself, other people, and that you can handle things when you're alone.
Show them that you have the money. Maybe they won't let you go because they doubt that you have the money. Make sure you have enough for food, gas if you're driving somewhere, plane tickets, and anything you might need along the way.
Talk to them. Find the right time to ask. If you ask at a bad time, the answer will be no, and no forever. Ask politely and maturely, explain carefully, and leave the whining, begging, and crying for your school's play. Make sure that you don't ask them repetitively, especially if they're in a bad mood. Tell them the dates, time, how you'll get there, etc.
Make sure it's absolutely fine with your friend. You don't want to invite yourself over. This is another sign that your parents could see as immaturity.