Remove all third-party skin packs from MBII directory.
Remove all third-party skin packs from base directory. Leave only assets*.pk3 files there.
MBII Launcher => Settings => check "Enable logging" => Repair installation.
Post latest log from "Jedi Academy\GameData\MBII_Launcher\logs" here.
Also, post a screenshot of those "distorted and broken models", so we can see it by our own eyes.
That would help to understand what's the reason of your issues.