In order for an imported model to function correctly, try doing this.
Ok, you've downloaded the model, make a new folder (It's what I do) and unzip the models into that new folder.
Start up World Editor and load up your map.
Open up Import Manager (F12) and click the little paper with a green arrow pointing to the left.
Browse to your new folder and import the MDX and BLP files.
Double click on the BLP files listed in the manager, a menu should pop up. See that little box on the new menu? Check it.
Import the correct custom path. Most of the time you either just have to delete the "war3mapimported\" or enter another path. Most of the time it's "Textures\". If so, then delete "war3mapimported\" and replace it with "Textures\". Models do not need to have their paths edited.
Save your map, close out, and reload World Editor. It should work. If you tried just deleting "war3mapimported\" and it didn't work, then try "Textures\", save, close, and reload. If it still doesn't work, go back to the page where you downloaded the model, it'll have the paths necessary.
Also, just in case, do not use the quotation marks for the paths.