I am a resident of NY. I was in Michigan for work in (Oct, Nov, Dec) 2018. Didnt change address. My W2 has my NY address, should i file my tax for Michigan state as well?

Yes.  You will file a Michigan nonresident return for the income you earned in Michigan.  However, if your main work is in NJ, you will need to subtract the Michigan income out of what might be reported to New Jersey.  Both New Jersey and Michigan cannot tax you at the same time on this income.  New York can and does tax all of your income.  If you work in NJ, prepare the returns in this order:

1. Figure out the MI income, and report that amount to Michigan on a MI nonresident return (since it is not marked on the W2, you will have to allocate or apportion, or manually enter the income as Michigan wages).
2. Prepare the NJ nonresident return, but override an income screen to subtract the Michigan income out of the NJ return.
3. Prepare the NY resident return.  If the first two returns are prepared first, you should have a credit calculate over to your NY return for taxes you pay to MI and NJ on the income attributable to each.  

Thank-you very much for that explanation 🙂

You are welcome.

I am a full time student in MI. In 2020, I had three part time jobs all for companies located in MI.

In one of the jobs,  the payroll company sends me a w2 with NY as the state (based on my permanent address) and deducted NY state taxes.

Should i ask the payroll company to send me another w2 with corrected information ? 

OR should i file MI as resident for the two jobs and a non resident NY return with the turbotax system generated income although the work was in MI