This doesn't explain it all, but here are a few factors:
Cheap pasture land in the sandhills has created a lot of wealth for cattle ranchers.
It's not oil, but the ogallala aquifer provides a valuable source of water to croplands in the Platte River Valley. The benefit is consistent crops every year. Alfalfa deep roots directly to the water table and row crops always have a source of irrigation.
Many small stakes investors in the state have evolved into millionaires largely due to buying a share or two of Berkshire Hathaway in the 70's & 80's. The local influence makes this more common than in most other states.