South
East and South.
To travel from the US state of South Dakota to Oklahoma, you would travel south.
You pass through North Dakota, South Dakota, Nebraska, Kansas, and Oklahoma. If you want to travel by Interstate, you would pass through North Dakota, South Dakota, Iowa, Missouri, Kansas, and Oklahoma.
Departing Texas you would travel north to reach South Dakota.
Departing South Dakota you would travel southeast to reach North Carolina.
Travel north.
Departing Texas you would travel north to reach South Dakota.
Kansas is farther south than South Dakota.
North
the direction is north.
You would travel due north.
That depends on where you are. Nebraska is northeast of Colorado, north of Kansas, south of South Dakota, and west of Iowa.