There are numerous alternatives between OKC and Chicago, or Tulsa and Chicago, several I use frequently, but not to avoid the short toll sections on I-44 in Oklahoma, rather to avoid certain congested places (like St Louis, or Kansas City, kind of have to choose, as avoiding both gets tricky).
One way is I-35 north through Wichita and Kansas City to DesMoines, then I-80 to Chicago, approaching west side. But that puts you on the Kansas Turnpike, where the tolls add up to more than the Turner and Will Rogers turnpikes in Oklahoma.
A variation on that is to take I-35 north out of KC as far as US-36, take that to Hannibal, then I-72 to Springfield, Illinois. From there you can take I-55 to the west side of Chicago, or stay on I-72 to Champaign, and take I-57 to approach the southern suburbs.
To avoid both KC and St Louis I will sometimes (from NE Oklahoma) follow US-54 through Missouri (I get it at Fort Scott, from OKC you'd connect at Wichita) either taking it all the way to I-72 in western Illinois, or going north in eastern Missouri to Hannibal (US-61 or Mo-19, which I used this last trip). Another way avoid KC is the west side, take K-4 NE from Topeka to Atchison, then US-59 to cross at St Joseph and connect with US-36. Or US-59 north from Lawrence, or US-75 or US-77 north to US-36 in Kansas.
A lot depends on your time budget. While there are not a lot of extra miles, staying off the Interstates form NE Oklahoma to Chicago or southern Michigan costs me an extra half day. However, it does save moneyon gas, because I'm often cruisin 50-60 mph, rather than trying to keep up with 70 mph traffic, maybe as high as 75 on Oklahoma turnpikes, 80 on the Kansas Turnpike, and yes, the big trucks in the "slow" lane are trying to push those speeds. But you go through some interesting places on US-54 or US-36, if you take the time to stop and visit.
In this part of the country we use the US-numbered highways as our main travel routes, we didn't get that many Interstates (except the ones that followed toll roads we had already built) and they are often a long way out of our way, from where we are to where we are going.
Tom Test
Itasca Spirit 29B