I'm playing FIFA 07 on XBOX.

On the game, the new Arsenal signing (subject to work permit, I know) Eduardo da Silva is listed in the Croatia team, but he does not have a club, as Dinamo Zagreb are not on the game.

Is there any way that I can assign him to the Arsenal team?

From what I Remember of the ingame editor, no there isn't a way to assign him to a club, but I would just try searching for him in the transfers window (or whatever it's called in the main menu, no in manager mode) and see if it brings him up.

Unfortunately the genious that is EA Sports decided to make Nat Team players who were on clubs not in the game (ie Eduardo) NOT available in any mode other than International games.

This sucks horribly.

The list of players we can't access is long, Eduardo, Sorin, Ustari etc.

You need to use a program such as Creation Master to edit the actual ingame database, then you can transfer whoever you want to ANY club team.

What EA should have done is take any database player NOT on a club & toss them into a huge FREE AGENT pool, that was users could transfer them in Career mode.

You need to use a program such as Creation Master to edit the actual ingame database, then you can transfer whoever you want to ANY club team
No help to the OP, who is playing on an X-Box

What EA should have done is take any database player NOT on a club & toss them into a huge FREE AGENT pool, that was users could transfer them in Career mode
That would cause some interesting and horrible side effects. I would prefer an 'internationals pool' for those players not assigned to a club team but only assigned to an international team (apologies for the pedantry but the preceding description and your own are subtly different in a very important way). I also don't like the idea of them being free agents, since it can safely be assumed that players of that level will belong to a club somewhere, and therefore should cost you a transfer fee to acquire.