I decided that I had quite a few mods, so I deleted the esp.s (and esm for one), with their mesh, texture and sound files, along with files of already deleted mods, after I tried to play oblivion, but when I clicked 'Play', the window came up only for a second or two though, and before I deleted the files it worked normally.

So is it possible that I deleted a necessary Oblivion file?

The obvious answer to your problem is to undelete them assuming you can do that (by opening your recycle bin & restoring them).
If you aren't able to do that then you may have to reinstall. Do you still have oblivion.esm?

ESMs are meant to be used by several mods. If some yet active mod rely on it the game can crash indeed.
So try restoring the mod that had the ESM you deleted and look if the game is able to start. If so, you will need to uninstall all mods that relies on that esm before trying to remove it.

Hmmmm. . .I'll try downloading the mods again as I have already emptied the bin. . .

It'll probably be better for you to reinstall, in my opinion.

From what you're saying, it sounds as though the game is crashing on startup. If that's true, then I'm pretty there's something wrong with Oblivion.esm. You should be able to launch the game regardless of what other esms you've loaded in previous saves.

I might be wrong, though.

I agree, if you have cleared your recycle bin, at this point it is better to just copy your save files to a safe location, then re-install the game. In the future, remember that it is always best to remove mods one by one. Get rid of any items that belong to that mod then save your game. Then deactivate it from the data menu and load your game. You'll get an error message but it's okay. Play your game for a few minutes and if there are not problems then save to a new slot. Carefully go through and remove the files that belong to the mod and delete the .esp. Then try your game again from the new save. You should not get the error the second time. Yes it's tedious, but it's much safer than just deleting files in bulk, but you see that now.

Well it is starting now that I have re-installed the deleted mod. . .but is there a way to remove all of a mod (the esm/esp, meshes, etc. . .) without upseting the oblivion start-up? I don't want to install oblivion again with the mods just because I lost one file. . .

Also how can a removed mesh/texture/sound file stop oblivion from working?

If the game crashes like that, it's because some mod's master file is missing.

Check the mods you still have enabled and see what mods they depend on. Probably, one of them is the one you deleted.

Either disable the dependent mod along with its master, or leave the master alone and play on.

Yeah, theoretically, you should be able to delete them as long as you delete the dependent mods as well.

Something no one has mentioned--is it possible the mods replaced, and subsequently left "vacant" after deletion, essential files in the directory structure, like meshes or something? Or if that were the case, maybe the game would still start and the affected mesh would just look weird.

No; and yes. All important files are stored in .bsa files.

All I can remember is deleting a mod sound file from Oblivion/sound (not Oblivion/Data/sound)

Except that the files in the BSA will no longer be used if something in the data folder has overwritten them, and you are using a saved game with those overwrites in place.

Since the game isn't starting, the only real solution is to do a fresh install, and only add the mods that you want to use. You may not like the idea, but sometimes, due to what mods add or change, this is the only solution. This is especially true since you were using a .esm which probably wasn't entirely self-contained. You may have also accidentally deleted some of the files needed by the vanilla game by accident. Not everything is stored in the BSAs.