The quickest route is I-35 to OK City, I-44 to Springfield.
There are a lot of alternative routes, Texas has a lot good roads, Oklahoma a selection of bad ones. The shortest, probably, is I-35E into Dallas, US-75 out of Dallas to US-69, then US-69 to pick up I-44 near Craig, Oklahoma. However, US-69 goes through a lot of slow places.
To miss Dallas entirely, you could take Texas 31 to Athens, Texas 19 to Paris, US-271 to the Indian Nation Turnpike, connecting with US-69 near Savanna and on to I-44. I've used this route (not the Texas 31 part) for years to avoid Dallas on my way to Houston, but I don't fool myself that this is a quicker route. When I need to get to Houston in a single day, it is US-75 to Dallas, I-45 to Houston (or book a flight on Southwest).
Tom Test
Itasca Spirit 29B