Is the U.S. state of Oklahoma considered a southern state?

Yes, Oklahoma is a southern state.
The U.S. Census Bureau classifies Oklahoma as a Southern state.

https://www2.census.gov/geo/pdfs/maps-data/maps/reference/us_regdiv.pdf

It is south of the Mason-Dixon line and, although not a state during the Civil War, many former confederates settled there after the War Between the States.

The Great Plains encompass a very small portion of Oklahoma. The culture of Oklahoma is predominantly southern. It was a hot destination for Southerners trying to escape reconstruction. It is clearly not Midwest as that is not a blanket category you put states you aren't sure of.

Hence why they U.S census bureau puts it in the South. No one claims it is as southern as Alabama, but it is more southern than not. SE OK is no different than the deep south.
Furthermore, this question is not a matter of opinion. Anyone spending any time in OK shouldn't need to ask this. Simple research could have also given you a better understanding.

For example:

Now, the Southern Focus Poll, conducted by the Institute for Research in Social Science at the University of North Carolina at Chapel Hill, provides strong support for including such states as Texas, Kentucky and Oklahoma in the South. On the other hand, West Virginia, Maryland, Missouri, Delaware and the District of Columbia don’t belong anymore, if they ever did.

https://www.eurekalert.org/pub_releases/1999-06/UoNC-USRW-020699.php

http://www.stats.indiana.edu/maptools/maps/boundary/census_regions.gif
Most of Oklahoma is not a flat vast wasteland like you see on storm chasers. Most of Oklahoma is heavily wooded and the average rainfall of OKC is 38 inches. The SE gets over 60.

Bottom line: The majority of Oklahomans call themselves southern. The culture, speech and cuisine is also southern. Oklahoma was a Confederate controlled territory during the war. All tribes in OK fought for the Confederacy. Oklahoma borders Arkansas, Texas and comes very close to Louisiana. Some of the more ridiculous notions is Southwestern. Living in OK most of my life with a stint in AZ, In can assure you there are no similarities between these states.You can find Sweet tea all over the state, unlike what the poster said above. Old cotton plantations were abundant in the SE portion and most of the towns in OK are named after towns in the old south. Oklahoma is part of what the south is today. The year is not 1864 and we don't still use the Mississippi to determine east and west.

100thmeridian.org/100thPDF.gif website no longer exists

Oklahoma is not part of the Historically Southern United States. Although, geographically it can be considered part of the Southern US as defined by the US Census Bureau, it is not part of the true South.
https://en.wikipedia.org/wiki/Southern_United_States#/media/File:Southern_United_States_Civil_War_map.png

I was born and raised in Mississippi and then went to college in Oklahoma. While living in Oklahoma, I found that some Oklahoma residents thought they were part of the Historical South. But as a native of the Historical South, we do not consider Oklahoma as part of the South, whatsoever. Bless your heart if you do.

Below is another map, which shows the South, culturally and historically speaking. It's the states that seceded from the Union. Oklahoma is not part of that. Living in both the South and in Oklahoma, I'd say that Oklahoma has country living, which a lot of the South does too - but it does not have the Southern culture.

http://www.worldbookonline.com/contents/common-content/wbe-content/pc/lg/lr004153.gif