Hola. I would say: Get in the car or get into the car....is fine. The last "ON" is never used unless you want someone on top of the car. 😁 Which would be unsafe and I don't suggest anyone riding on top of a vehicle. For the last three: I should be home I should be at home "I should be in home" is the wrong preposition to use and sounds unnatural. Hope that helps. Tengas un buen dia.

I should be home or at home. Get in/into the car ;)

Get in the car is 💯 correct one, should be home and should be at home are both correct.

Get in the car is correct

So get into the car is correct. Get on the car means to get on the roof of the car. I should be at home and I should be home both are correct but in home is 100% wrong