The original English from which this bit of kid-speak descended appears to have been something along the lines of "All ye, all ye out are in free". That is to say, all the players who remain out hiding in the yard are free to come back to the starting point, without being caught out.

In an early Peanuts comic strip, an unfortunate Linus van Pelt rendered this call as as "Ollie Ollie Olsen Free-O". This elicited a great deal of mockery from Lucy, who corrected him with "All-ee, all-ee, out are in free."

When I was in grade school, the call was "All-ee, all-ee, out's in free."

Judging from a softlink at "Ali Ali Oxen free", it seems that someone thinks this expression came from the Biblical "Eli, Eli, lama sabachthani?" (Jesus's "My God, My God, why have you abandoned me?") This strikes me as an amusing, but highly unlikely, etymological possibility.