I recently installed a few mods to make my Morrowind experience a bit more interesting. I installed them as directed, and activated them in the Data Files section of the launcher.

However, when I started up, it gave a message that one or more of the plugins could not find the master file they rely on (or something vaguely to this tune), and to consult the warnings.txt for more information; I did, and this is what I got:

One of the files that "Samurai Pack Ver2.esp" is dependent on has changed since the last save.
This may result in errors. Saving again will clear this message
but not necessarily fix any errors.
One of the files that "Bloodlust.esp" is dependent on has changed since the last save.
This may result in errors. Saving again will clear this message
but not necessarily fix any errors.
One of the files that "Dodge Mod 1.2-WD (Enhanced-LD) (Tribunal).esp" is dependent on has changed since the last save.
This may result in errors. Saving again will clear this message
but not necessarily fix any errors.
One or more plugins could not find the correct versions of the master files they depend on. Errors may occur during load or game play. Check the "Warnings.txt" file for more information.

Anyone know what I have to do to remedy this situation?

I think it's because the mods were made in a different version of Morrowind (i.e. before the last update).
Does it stop the game from starting up completely, or do you just have to click through a lot of things? And does it bugger up the game while you're playing?

Basically, I get the message when It starts up, then nothing else. The plug-ins seem to function fine, but my game keeps on crashing to the desktop without warning.

That's pretty normal with Morrowind, unless it happens consistently at one particular point. It likes crashing for no discernable reason. Just click through those errors.

it seems to have a special preference for crashing as I start a new game.
The dunmer guy who wakes you up just about gets through the first five seconds of his speech before I get a weird noise and it suddenly goes back to desktop.

Sounds like a mod problem. First, make sure that, if you don't have both expansions, no mods need them. Then ensure you're patched, and experiment with removing mods until you find which one's not working properly.

Binary search algorithm for finding defective mods:
Uninstall the first half of the mods. If this solves the problem, reinstall half of those you uninstalled and test. If it doesn't, install the uninstalled ones, and uninstall half of those you kept installed, and test. Continue applying algorithm until you find the one that's not working. It's much quicker than simply going through each mod and uninstalling it to see if it solves the problem.

Just showing my university education is worth the money. :D But that's the procedure I use.

Okay, I'll try that and get back.
But first: Sleep!

Just ignore those messages, i get them too, but nothing really happens during the game.

Oookay.
It seems that, even without ANY of the mods active, my game still packs up within the first few seconds. Now I'm just confused.

Might warrant a reinstall, then. Sometimes things like that just happen.