Another lyrics legal question

Are you allowed to publish translations of a song without any permission?

The answer is a definite: NO.
There are, however. some people who have no idea about the Copyright laws of the different countries. Usually the publishing house for any writer will put something similar as follows:
"This book may not be reproduced in whole or part thereof, or stored in computers, or other electronic divices by any means, without the written permission of the author or publisher, or both, except in the case of a brief quotation (not exceeding 100 words), and only when used for critical articles and reviews.
The author has the sole right and ownership, and may grant permission for a one time use, by a signed document from him/her.

Greetings
Ina

The possible exception would be if YOU do the translation and the tune is not copyrighted.

I ran into this at my church, cataloging the copyrights for all the songs we do. How Great Thou Art is but one translation of the original, copyrighted, Swedish "O Store Gud", which has also been translated, and separately copyrighted, in Russian and German. In fact, How Great Thou Art is actually a paraphrase with a couple of new verses. There's a direct translation, "O Great God", that has its own copyright.

The only way these translations each manage to have their own copyright while using the same tune is because the original tune comes from a Swedish folk song that is not copyrighted.

"How Great Thou Art" is by Stuart K.Hine, both the music and the words, copyrighted in 1953.
Re-copyrighted in 1981 by Manna Music Inc., 2558010 Stanford Ave, Valencia,California, USA 91355
International copyright secured, all rights reserved. Used by permission..

In my church all songs taken from anywhere, always have the copyright information given, and all the credit is given to the author.
Usually in North-America the copyright laws are in place as long as the author lives and 35 years thereafter. Covered by International copyright laws, the Library of Congress in Washington, DC., USA. in conjunction with the same type of library in Paris, France. These two places are the only two organizations, who issue ISBN numbers for all works. And with this number, they also issue the copyright.
Any music, that anyone wants to translate (use) will have to be done this way, and I quote Zondervan Publishing House: "It can only be used by permission of the publishing house." unquote
Even re-productions have to be done by permission.

Greetings
Ina

One key note here is 'Public Domain.' If a song is printed with that annotation then it's ok to print song lyrics any way you like. That applies to a lot of old church songs.

This is such a complicated issue because it's not like you claim you wrote the song
and also copyright law differs from country to country

NO, you can not do that without any permission.
First of all, there is clearly a copyright issue here!

As well as this, you need the original author's approval of the translation itself.