Norman has an Amtrak station (NOR) located just north of campus that is served by the Heartland Flyer.  This train has daily service out of Dallas-Fort Worth (FTW) departing at 5:25pm and arriving at 8:48pm, all for about $22-42 one-way (depending on discounts).

The Texas Eagle connects Dallas-Fort Worth to Chicago, New Orleans, and Los Angeles, and has sleeper cars available for those long stretches.