Every interstate in and out of Tulsa is a toll road. This includes the Muskogee turnpike, as well as I-44 from Joplin in the Northeast to Oklahoma city in the southwest.
For the Muskogee turnpike, there will be 2 toll booths....one between I-40 and Muskogee, and another between Muskogee and Tulsa. The only break in the toll road is when you pass thru Muskogee. At this point, the speed limit drops from 75 to 70.
The toll should be somewhere between $1.25 and $1.75 per leg. I'm not sure as I haven't traveled that route in a year.
There is no better way into Tulsa from the southeast.