It sounds like you are on the right track. In order to get any of the state withholdings back from NE and IA, you would need to file a non-resident return for those states. Be sure to complete these returns before completing the IL resident tax return so that the credit for taxes paid to another state will be the correct amounts.
It is not necessary to do anything other than file a non-resident return for IA even though there is a reciprocal agreement for IA and IL. If this job situation was more long-term, then it would make sense to take advantage of the reciprocal agreement and have IL taxes withheld from the IA wages so that two state returns would not be required.
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