It wouldn't be unusual, in fact it's quite likely you would owe the state.
The total of your state withholding on ALL of them must cover the state taxes owed for ALL of your income.
A short-term job employer might not withhold any, or only a low amount of state income taxes if the job is short-term, because each employer will not be taking your income from the other jobs into consideration when they set your state withholding level. SO, if you take multiple W-2 jobs during the year, you will have to remember to submit a W-4 form with zero for it's allowances, so that the employer withholds more state income taxes.
BUT...4 W-2 forms? Really? Why?
IF one employer sent you multiple copies...there are usually extra paper forms for the state(s) involved...but they still go on only one W-2 in the software (or if one is a corrected form W-2C, the corrections go onto the one W-2 in the software and there is a checkbox to check to indicate it is corrected.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
