Working out of state

Ohio internship was a nonresident position*. Much of Ohio has city taxes if you work or live in the city. Ohio city and state returns need to be filed as nonresident. See Which city tax returns can I do in the TurboTax state program?

*depending on parents

NY and CA were both for college. 

• If the parents claim the student, the student lives in their state and just attends college. 
• If the parents are not claiming the student, file where student is a resident.

The student will file a resident return in the home state, driver's license, voting, intent to return, family, etc.

To make sure I understand correctly:

If the parents are CA residents and claim the child as a dependent, then the child needs to file an OH state and city tax return as a nonresident and also file a CA tax return on the same income as a resident of CA? Isn't that double taxation? Filing a CA tax return for the student without having withholdings for CA automatically trigers a balance due, even with the small credit for the taxes paid to OH.

Yes, file both states. It isn't double taxation because you are getting a credit for the tax paid OH. CA just has a higher tax rate. 

You get credit for the lower state tax on the lowest taxable amount.

• Each state calculates taxable income differently. 
• Each state has its own tax rate/ system.
• You get the lowest of both categories as a tax credit.

CA shares information with the federal government and they will know you filed federal and wonder why you didn't file CA. They would then aggressively send letters and penalties. CA will always get their money.