At the first step of my Omeka install I get the error:
Unknown MySQL server host 'mysql-50.int.mythic-beasts.com:3306' (1)
I have tried a few variations on this (explicit port param instead of part of the hostname), but always the same error.
I can connect using MySQL (DB) and PHP on the command line. The MySQL server is on another physical machine. I am running PHP 5.2.14 with fastCGI, and the latest stable Omeka.
Are your Omeka installation and your database on different servers? I'm not sure if that will work, but I may be misunderstanding what you have said.
It definitely won't work to include the port as a part of the hostname. The port should only go in the port line, with the semicolon removed. With port 3306, you shouldn't actually need to include the port at all, since that's the default.
Omeka uses fairly bog-standard code for connecting to the database, you shouldn't need to do anything special or different, and there's also nothing that should prevent you from using a MySQL server that's on a different machine.
You're sure that your host and port parameters are correct and in the right places in db.ini? You could post your db.ini with your username and password omitted if it's still not working.