"Yes marry have I" usage

In this passage, marry¹ is not used as an oath or as a term of surprise; it is used as an interjection meaning “certainly”. Wiktionary gives definition “(obsolete) indeed!, in truth!; a term of asseveration”, and illustrates with a quotation from Shakespeare’s Henry IV: “I have chequed him for it, and the young lion repents; marry, not in ashes and sackcloth, but in new silk and old sack.”

This is marry the interjection, which is originally a minced oath. According to OEtmD, the term is an obsolete corruption of the name of Mary, the mother of Jesus.

Shakespeare was fond enough of marry used in this way – and also of the unminced oath by God’s Mother – that both appear in various glossaries of archaic words found in his plays.

A fair reading of the text would be:

Baa, baa, black sheep, / Have you any wool?
Yes, by Mary, have I, / Three bags full.

This usage of marry is hopelessly obsolete. It's just an interjection (derived from The Virgin Mary, so you could call it a minced oath) that was used to express surprise - in this case, the sheep obviously would be surprised to be asked if he had any wool!

A more modern equivalent would be indeed. A much more modern one would be absolutely.

There's also archaic word-order, and I doubt you'd often hear "my master" today (even less "my dame"). In modern English (ignoring scansion issues) the reply would start

"Absolutely! I have three full bags!"

Also note that as a nursery rhyme today, the third line is invariably "Yes sir, yes sir", because no-one is interested in teaching their kids about that archaic use of marry.

Only the one line that you pointed out looks archaic to me. "Marry" is an archaic interjection which was used as an exclamation of surprise or emphasis. "Have I" is just the switching around of the words. It would read, in modern English, "Yes, I have three bags full."