Sayings

Some of these can be found by searching www.google.com (e.g. "cliche origin"), or try www.phrases.org.uk.

Heaven's to Betsy

Olly olly oxen free

But first, here is an email I got 7/8/2007 from David Eyerly:
All Ye, All Ye Outs, in Free.

It was common for the town crier to pre-phrase a declaration with “All Ye, All ye” meaning that all the citizens of the town needed to be aware of the information the crier was about to state. Typically the town crier would yell this as a pre-amble to a message from a King, or court, or other high official. The townsfolk would gather to hear the pronouncement (it was rarely an announcement!) Circa 1600, England. This migrated to 1650 Penn settlements.

“Outs” were those not yet “in”. (Those un-caught in a childs game.)

That they were able to come (to the town square, or base) without penalty was the pronouncement. “Free.”

Thus, “All ye! All ye! Outs in free.” Which the Dutch children in Pennsylvania then corrupted to the best English they knew. Over the years the phrase you mentioned became meaningless, except that the concept remained the same. The “outs” were now “in free.”
- End David Eyerly's email.

Using www.google.com to search, the best web page I've found on this is www.phrases.org.uk/bulletin_board/4/messages/992.html, as follows:

Lots and lots of theories from lots and lots of sites. Most from Jesse at Random House:

1. The phrase is used in a variety of children's chasing games, especially hide-and-(go-)seek. The rough form of this game is that a player (called "it") gives other players a chance to hide, and then tries to find them. When "it" finds the first hider, he calls out some phrase indicating that the other players are "safe" to return "home," at which point the person "it" found will succeed him as "it."
The original form of the phrase was something like all in free or all's out come in free, both standing for something like all who are out can come in free. These phrases got modified to all-ee all-ee (all) in free or all-ee all-ee out(s) in free; the -ee is added, and the all is repeated, for audibility and rhythm.
From here the number of variants takes off, and we start seeing folk etymologies in various forms. The most common of these has oxen replacing out(s) in, giving all-ee all-ee oxen free; with the all-ee reinterpreted as the name Ollie, we arrive at the phrase, which, according to the Dictionary of American Regional English, is especially common in California. Norwegian settlement areas have Ole Ole Olsen's free. For the out(s) in phrase, we also see ocean, oxford, ax in, awk in, and even oops all in.

2. One guess is that the original was something like "all in free" for "all who are out can come in free", to indicate that the person who is "it" in the game of hide-and-seek has caught somebody to become the new "it", and so everybody else can come out of hiding without the risk of being caught.
Oral transmission has garbled this in fascinating ways, with all in, for example, being translated by a series of mishearings to the name Ollie (short for Oliver, once more common than it is now). And oxen may have come from an intermediate form out's in free - other recorded versions are awk in, Oxford, and ocean.
Various subscribers remember versions that suggest the first part of the catch was once something like "all of you". Charles Wilson wrote: "When I was growing up in the American South we actually said, 'All ye all ye outs in free' when playing hide-and-seek (although we called it 'hide-and-go-seek)".