I finally got it to work :-) I'm sure I tried this scheme before where it didn't work, so perhaps I forgot something in the process of deploying the first time I tried it.

The Jaybird FirebirdSQL-1.5.6JDK_1.3 package was the one that worked for me. A note for Jdeveloper newbies: Setting "Deployed by default" in the JDeveloper project properties for the Jaybird library does not seem to work. I had to add it to the Contributers list in the properties for the deployed jar.

What confused me a bit when testing java from command prompt locally, was that JDeveloper uses its own java version. So things could work using Jdeveloper, while it failed using java from a command prompt.

I used this program code to obtain a connection:

String url = "jdbc:firebirdsql://the.firbirddbhost.com:3050/firebirdalias";
Class.forName("org.firebirdsql.jdbc.FBDriver");
Connection fbConnection = DriverManager.getConnection(url, fbusername, fbpassword);

Having the Jaybird drivers included in the deployed jar, all I needed to run the app was:

java –jar filename_of_jar

Thanks to Mark and Roman for trying to help me.
(by the way, it was a 32bit Windows 2003 server)