The version above is from an old book. Some of the spelling has changed. See explanations below...

*"Begge" seems to be the old Swedish spelling of "both". It's now spelled "bägge". The words "bägge" and "både" are interchangable. Each word means "both", and each word is in current usage.
**"Halven" is a typographical error. It should be "kalven", meaning calf.

"Visan" literally means "the song", but it can also mean "the story".
"All" literally means "all", but it can also mean "over/finished/at an end".

You could translate it as:

An old man and woman owned a calf,
And that's half the story,
They took it away to graze,
And now the story is over.

Thanks and Acknowledgements

This rhyme can be found in "Svenska fornsånger: en samling af kämpavisor, folk-visor, lekar och dansar, samt barn-och vall-sånger, Volume 3" (1842) by Adolph Iwar Arwidsson.

Translated by Mama Lisa.

Tack så mycket!