Help fix meals at home, clip coupons for things you actually use, limit your water use (showers, baths, washing dishes) run the washer when it's full, turn out lights in rooms that no one is in. See what "non-traditional" opportunities are out there to do crafts for consignment or develop a skill that people would be willing to compensate you for.
You're a sweetheart. Your Dad doesn't want you to help with the bills, though. Just make his life easier at home. The old man is probably going to be working hard trying to find another job and you can help by keeping the house clean, spending time with him doing yard work, and things like that. Tending to that minutia will let him concentrate on his job search.
i mow lawns for 25$ a yard and walk dogs 15$ an hour but if these are good for you you can try helping around houses and or a website called swagbucks i made a 300$ gift card in less than 2 months
Selling drugs, prostitution, stealing things from stores to pawn (only try this when they're busy).
face the facts, you are unable in your position to help your dad, although your emotional desires are appropriate. You might want to babysit (if you know how) but your parents will have to claim taxes on your earnings.
Well I would just help maybe start a lemonade stand