I'm totally in love with these tools - what are the best equivalents that are compatible with Morrowind?

I haven't used those tools before. For Morrowind, there is http://code.google.com/p/mlox/wiki/Mlox (for ordering mods), http://www.uesp.net/wiki/Tes3Mod:Wrye_Mash (for mod management), and a host of alternative mod editors - such as http://code.google.com/p/mlox/wiki/Tes3cmd, http://planetelderscrolls.gamespy.com/View.php?view=other.detail&id=52, and http://www.uesp.net/wiki/Tes3Mod:MWEdit. I'm sure someone will be along shortly with a more detailed explanation, if you require one.

edit: punctuation + added alternative editor links

Mlox, Wrye Mash, and Enchanted Editor are the three tools that closest resemble ModOrganizer & TES5/FNVEdit for Morrowind. Morrowind mods aren't as complex as later TES mods, so most conflicts can be fixed via the CS. You'll definitely want to use WM's merged leveled lists if you use two or more mods that add or make changes to leveled lists. Unfortunately WM's merged patch doesn't work like a Bashed patch, so you'll either need to use EE or the CS to merge conflicting mods.

The http://www.gamesas.com/topic/1305729-mod-recommendations-for-new-players/ has a section on Tools. (and lots of other info)
The second post has advanced tools, but they are more for editing mods, not using.

As others say, you'll just need to learn Wrye Mash and Mlox to begin with.
And a tool to clean mods, as many are dirty.

I suggest using the "Wrye Mash stand alone" version (link in pinned thread)
It is the simplest to install.

I would also consider http://mw.modhistory.com/download--5234 to be essential for its merged objects function for those times when 2 mods make different changes to the same object (i.e. one changes value and another changes weight of the same object)