In general, you pay income tax in the state where you earned the income, so if you live and work in Oklahoma you would report and pay tax to Oklahoma.  Nebraska has an exemption if no essential services or activities are required to be performed in Nebraska AND the services or activities required to complete the project will be performed predominantly in a state other than Nebraska, so you may not have to report any income in Nebraska.  (You can check with your employer if you are not sure.)

If you did not travel to Nebraska at all, you would only report to Oklahoma.

according to taxfoundation.org, Nebraska follows the “convenience of the employer” rule, which taxes telecommuters based on where their employer’s office is located.  So, according to this, you would have to pay NE taxes.  However, since you likely have to pay OK taxes, one state will give you a credit for taxes filed in another state.  I don't know which one takes precedence.