This is a summary of the process of how to setup a multilingual site with domain access. Please feel free to edit any parts which are incorrect or that may confuse users. Content is based on how we made our sites work and on this tutorial by Jose Reyero:
http://reyero.net/drupal/internationalization_domain_access_multilingual...

If you have installed Domain Access and all seems to work fine, but then you want some domains (or subdomains) to be in different languages, for example:
- maindomain.com (english)
- sub.domain.com (french)
- domain2.net (spanish)
- sub.domain2.net (spanish)
- domain3.com (english)
- domain4.org (german), etc.

The following is assuming you correctly setup your affiliate domains and/or subdomains in your settings.php file.

Change the default language
1. Enable the correct modules (Domain Access, Domain Variable, Domain Locale, Internationalization & Variable). See links to these modules at the end of this page.

2. Enable the languages you will be using here: admin/config/regional/language

3. Enable URL detection method here (must be Path prefix): admin/config/regional/language/configure

The following sub-pages contains How-To's to extend and customize Translation Management Tools.

This is the approach I have followed, there might be others :

This works with 2 languages and the principle is the same with more languages. The idea is to create one new block per language and to invoke some php code to insert the user login block content.

Some external links and articles about Drupal 6 and i18n: