Links to Nebraska government agencies, statutes, regulations, cases, etc. are posted by Washlaw and FindLaw. Primary legal materials are also available from Lexis, Westlaw and LOIS. Subscription services Versuslaw Fastcase have cases back to 1950; Google Scholar has cases back to 1950 for free. Supreme and appellate court cases are published in the North Western Reporter.
To check on the status of a pending bill, pull up the History with the Nebraska legislature's Bills and Resolutions search. For questions about pending legislation, call the Clerk of the Legislature's Office at 402-471-2709, 402-471-2271 or, in state, call 1-800-742-7456
"Legal Research Tools for the Nebraska Practitioner: An Annotated Bibliography" was published in 70(3) Nebraska Law Review 519-554 (1991). It's old but still useful for historical information.
For questions about Nebraska legal materials, copies and/or inter-library loan, try calling the Nebraska State Library (402-471-3189) or the University of Nebraska's Law Library (402-472-3547).