Like it or not, in Ohio, you are not considered to be an adult until you are 18 years of age. You may petition the County Family Court for an order of emancipation which would allow you to be on your own before you are 18 - but the court will only grant that order if you show the court that you are truly self-sufficient. This means that you can consistently provide for your own needs - shelter, food, medicine, transportation, education, clothing, etc. This is a difficult burden for many minor children to meet.
I assume from how the question was structured that you father has custody. Therefore, it is necessary that he agree to any "move" into another's household because he is still liable and responsible for you. If the other household takes you "in" without his permission, they could be exposed to legal consequences for interfering with custody.
If the reason you “need to get out” is because of abuse or neglect, then you can talk to the County Children’s Services Department and if the situation is sufficiently serious, the department may petition the court for temporary orders in your behalf whereby the court would then place you into protective custody. If the Court grants that order, Children’s Services would generally place you with another family member (after having been investigated and determined to be suitable).
If the reason you “need to get out” has to do with your disagreement over the rules your father has imposed, then I recommend that you talk to your father about family counseling. You may find that helpful in conveying to him why you feel the way you do — and you may actually learn why he believes that the rules are appropriate.
If your father agrees to the move, the family members that "take you in" should consider obtaining custody or guardianship over you. Also be aware that if the other family members reside in a different school district, you may have additional issues with enrollment as well as eligability issues if you participate in sports.
No you cannot legally do so without your guardian's permission.
However, the first response provides some incorrect information. There is no emancipation statute in Ohio, so you cannot petition the court to consider you an adult prior to age 18.
This answer is being provided as general advice only and is not to be relied upon for specific circumstances. By answering the question, no attorney-client relationship is created. As for any matter, it is best to seek consultation in person with an attorney who practices in the area of law in which you are inquiring.