A hit by a Shadow reduces my Strength by 1d4. Wearing the Gauntlets of Ogre Power, will I only notice the change when my (natural) STR score drops to zero? I.e. being hit by a shadow, losing STR in the process, on my next attack will I still attack with 19 STR?
Looking at the description of Gauntlets of Ogre Power in the DMG, page 171 (emphasis is mine):
Your Strength score is 19 while you wear these gauntlets. They have no effect on you if your Strength is already 19 or higher.
This mentions nothing about what happens if your "natural" Strength gets reduced to 0, so I read that to mean that all the time you are wearing these, you get to proceed using a Strength of 19.