They don't have a literal meaning and are simply expressions of strong feeling.
Origin:
The origin of "Well, I swan" is uncertain, but it's likely a shortened version of "Well, I swan upon my word!" which was a more formal exclamation used in the past.
Usage:
You might say "Well, I swear" or "Well, I swan" in situations like:
* Seeing something unexpected or unusual
* Hearing surprising news
* Experiencing something particularly impressive or enjoyable
Example:
"Well, I swan, look at that amazing sunset!"