That's an interesting question. As WEAO, it signed on in April 1922. That puts it after KDKA and WBZ, which have remained under consistent ownership since 1920 and 1921, respectively. (Yes, the name of the licensee has changed, but remember that in 1995 it was Westinghouse buying CBS and taking the CBS name, not the other way around.)
WBAA at Purdue goes back to early 1922 and has never changed owners, ditto for WGAZ/WSBT South Bend, which has been in the hands of the South Bend Tribune/Schurz family since early 1922. Then there's WHA Madison, which has been in the hands of the University of Wisconsin since 1921. WLB/KUOM Minneapolis (U of Minn.), WOI Ames (Iowa State College/University) and WHAA/WSUI Iowa City (U of Iowa) also go back to 1922.
It's safe to say that WOSU(AM) was one of the ten oldest stations in the country still in the hands of its original owner.