Let me start with a correction:
The name of the game that I have observed in the Pittsburgh, PA area 1980s to 2004 is "Strolla Ola Ola" not "Srolla.." Sorry about that.

(Correction made. -Joe Offer-)

"Strolla Ola Ola" and "Slap Billeola" both have the same tune. That tune sounds to me very much like if not the same as "Ring Around The Rosie".

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I have tried to find print versions of any one of these songs or their variants, or rhymes that are performed in this manner.
I know that I have seen "Stella Ola Ola" written down somewhere-maybe it was those Scout websites that Guest referred to in her {or his} post.

For the sake of those interested in traking down these rhyme research [or interested in books on or containing rhymes performed by African Americans, non-African Americans, and/or Afro-Caribbeans, it may be helpful for me to list the collections I've carefully looked through that don't include "Stella Ella Ola" type rhymes or other rhymes that are performed like them:
Dr. Thomas Talley's 1922 "Negro Folk Rhymes"; Dorothy Scarborough's 1925 "In Search of Negro Folk Songs"; Byron Forbush and Harry Allen's 1927 "The Book of Games For Home, School, and Playground"; Altona Trent Johns' 1944 "Play Songs of The Deep South";
Roger Abraham's 1969 "Jump-Rope Rhyme Dictionary"; Bessie Jones and Bess Hawes Lomax's 1972 "Step It Down"; Eleanor Fulton and Pat Smith's 1978 "Let's Slice The Ice"; ;Barbara Michels & Bettye White's 1983 "Apples On A Stick, Folklore Of Black Children"; Linda Goss and Marion Barnes' Talk That Talk"; Cheryl Warren Mattox's Shake It To The One That You love The Best"; Dr. Darlene Powell Hopson, Dr. Derek Hopson, and Thomas Clavin's 1996 Juba This $ Juba That, 100 African American Games for Children"; Grace Hallworth's 1996 "Down By The River, Afro-Caribbean Rhymes, Games, and Songs for Children"; and Alan Lomax, J.D.Elder, and Bess Lomax Hawe's 1997 "Brown Girl In A Ring"; collection of Caribbean rhymes.

I just recently borrowed a copy of Dena Epstein's " 1977 "Sinful Tunes and Spiritual" and haven't read it cover to cover, but these rhymes also didn't appear to be in that book.
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For what it's worth, I don't recall reciting "Stella" or "Strolla" or "Slap Billyola", * "Strolla Ola Ola" and "Slap Billeola"

*I like the "Billyola" spelling and will use it hence forth...but it actually doesn't matter how it's spelled-what really amtters is how it's pronounced..

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It's my emerging theory that these rhymes evolved from the stone passing/pounding games men played during nine day wakes {or Pass Plays" in the Caribbean. [The name "Pass Play" probably referring to passing the time while playing and not the act of passing a stone from one man sitting in a circle to another}. However, I'm not even sure if there were chants that accompanied these games. Does anyone have any information on this?

I also think that these "getting a player out" chants may have evolved from hand slapping counting out games such as this one from Trinidad that I am quoting from Nina Miller's 1965 "Children's Games In Many Lands" {New York, Friendship Press, p. 121}:

"One player stands with his hand held out, palm down, breast high. The other players hold their pointer fingers under the palm, touching it. The player who is holding out his hands repeats this rhyme:
                  Ziggeddy, ziggeddy
                  Marble stone.
                  Pointer, pointer, bouff!
                  Kisskillindy, kisskilindy,
                  Pa...Pa...poriff!

end of quote.
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Some of the words of "Strolla", "Stella", "Slap Billyola" sound Spanish to me. I'm still wondering if there is any Spanish connection...