I just, by chance, found your message. I am of the same obscure Oiler line. It is seldom I see anyone asking for info for this branch.
My ggg grandfather, George R Oiler, was the brother to Rachel. The other siblings were Catherine, Nancy, Elija, Harriet A., Miles T. and, John A.
Harriet married Joseph Stephenson, brother to Rachel's husband Thomas. Who were the children of Rachel & Thomas and did they stay in West Virginia or did they come to Ohio like here brothers?
By the way, not sure if you know Rachel's middle name is Virginia.
I am also at a loss for Elisha's parents. I have found school enrollment records for George. He was enrolled in Monroe Co., (W)Va by a Uriah Oiler. I don't know how Uriah was related though.
Charlotte's dad was Robert Howard. (I'm sure I have her mother's info here as well. It's just burried in a closet right now) She was born around 1814 in Virginia. In 1880 she is found on the Census in Lick Twp., Jackson Co., OH, as a widow living with her son Miles and his family. Her parents birthplace is listed as Virginia.
Elisha & Charlotte were married April 14, 1831 in Bedford, Virginia. Familysearch.org also lists April 11, 1831 in Rocky Mount, Virginia. But I'm almost certain this is when they got their marriage license.