Solved.
The default widget was problematic, as I ended up with a start page that was in one language that I could not change, or then it was in three languages (fi+sv+en) - of course giving me all the subpages three times. I wanted it in ONE language and then I wanted to change it, if need be. I tried several combinations of the Gengo settings (allow/disallow multiple languages; show in one/all languages; let Gengo decide). Nothing seemed to work and I felt lost without extensive documentation. Nothing new...
Then I found the language_control function and edited the gengo.php. That helped a little. I could add/remove languages and save, and after that I had those languages visible that I wanted. But it was inconvenient.
The solution was simpler than I could imagine:
I created a text widget with hyperlinks to http://blog.net/XX, http://blog.net/XY, http://blog.net/XZ (where XX,XY,XZ are language codes) using IMG tags to insert polyglot flags.
Now I have Gengo set to display all pages in one default language, finnish, first. Then I can use these links to switch languages.
I also needed to edit my theme to add /"<?php the_language_code(); ?>" at the end of the blogname (that works as a link to the posts page) in the header.
This works like a charm.
I'll need to work on some widgets still, to have their headers translated. And the contents of some widgets will pose a challenge...
Anyway, I can achieve what I want with Gengo.