Jesse was the son of John Oshall and Margaret Chambers Sterret. He married Sarah Elizabeth Smith on 15 Feb 1858 in Tippecanoe County, Indiana. They had fifteen children:
Alice, Catherine O., John, Jessie May, George Elmer, Jennie Evaline, Mary, Albert J., William, Lydia Viola, Ida Cenora, Olive Aldora, Emma Ellen Pearle, Lillian Florence, Emmett Cleveland.

Of these children Catherine died at age 6, and Jessie, Mary, and William died as infants.

Jesse served in the Union Army during the Civil War. He volunteered 19 Dec 1863 and was mustered in at Indianapolis, IN. His enlistment papers described him as about 6 feet tall with gray eyes, dark hair and dark complexion. He served as a private in Co. G 72nd Reg. Ind. Infantry, and later in Co. I, 44th Reg. Ind. Infantry. In May, 1864, Jesse was injured near Resaca, Georgia, when his horse fell on him during a charge. He was hospitalized for several months in Columbia, Tennessee with back and chest injuries and later received a pension for these injuries. He was discharged 14 Sep 1865 in Nashville, TN.

The family moved from Indiana to Woodson County, Kansas in the fall of 1876.

Death Notice, Chanute Tribune
Jesse Oshel 82 years of age, died last night at the home of his son, A. J. Oshel, three and a half miles east of this city. The funeral will be held from the son's home Wednesday morning at 10 o'clock. The services will be conducted by the Rev. W. W. Searcy of the First Baptist Church. The body will be taken to Welda for burial. Mr. Oshel is survived by six daughters and four sons. The children are Mrs. Alice Meats of Eugene, Ore., John Oshel, St. Paul, Kas., George Oshel, Chanute, Mrs. Eva Hecox, Haviland, Kas., A. J. Oshel, Chanute, Mrs. Viola Long, Indepence, Mo., Mrs. Olive Melton, Iola, Mrs. Pearl Minor, Gas City, Mrs. Lillian McClure, LaHarpe, E. C. Oshel, Fall River, Kas.

One of his granddaughters wrote this recollection of Jesse,
"When I was a little girl, I loved to hear him tell about things that happened in the war. He was Scotch and Irish. Instead of him saying, "I said," He would say "and says I." He was a jolly good man, my Grandfather."