For years I have collected the lyrics/tunes to unusual songs. I understand this is an Irish folk song, based on a true story. I don´t know, I never researched it. Here goes:
Welia, Welia, Walia.

There was an old woman & she lived in the wood, welia, welia , walia,
There was an old woman and she lived in the wood,
down by the river sawyer

Well she had a baby three moths old, welia, welia walia,
she had a baby three months old,
down by the river sawyer

And she had a penknife, long and sharp, welia, welia, walia,
she had a penknife, long and sharp,
down by the river sawyer.

and she stuck the penknife in the babys heart, welia, welia walia,
she stuck the penknife in the babys heart,
down by the river sawyer

There were three loud knocks come a knocking at the door, welia, welia, walia,
three loud knocks come a knocking at the door,
down by the river sawyer.

There were two policemen and a special branchman, welia, welia, walia,
two policemen and a special branchman,
down by the river sawyer.

So they put a rope around her neck, welia, welia, walia,
they put a rope around her neck,
down by the river sawyer.

Well the pulled the rope and she got hung, welia, welia, walia,
they pulled the rope and she got hung,
down by the river sawyer.

Well that was the end of the woman in the wood, welia, welia, walia,
and that was the end of the baby too,
down by the river sawyer.