From where in Oklahoma? The state is almost 300 miles wide.
From the eastern part of the state I use US-75 or US-69 and Indian Nation Turnpike and US-271 down to Paris, Texas-19 to Huntsville, when my destination is Houston. This bypasses Dallas area by a wide margin.
Getting to the Texas Gulf Coast without going through Houston depends on your destination. Going to Galveston means going to Houston. But if coming from western Oklahoma and going to Corpus Christi or further south, US-281 out of Wichita Falls bypasses Dallas by a large margin, taking you to San Antonio where I-37 gets you to the coast or I-35 gets you to Laredo. San Antonio is its own traffic problem, but nothing like Dallas or Houston.