[RPG] Do “Gauntlets of Ogre Power” keep the STR at 19 when I’m attacked by Shadows

The Strength reduction would likely only affect your beast form

Jeremy Crawford has said this regarding maximum hit point reduction (borrowed from this answer to a question about maximum hit point reduction):

Jonathan Longstaff
^@pukunui81
@JeremyECrawford What happens when a wildshaped druid that has had its HP max reduced reverts back to normal? Does the reduction carry over?

Jeremy Crawford
^{@JeremyECrawford}
Wild Shape—a reduction to hp maximum doesn't carry over from your beast form to your true form or vice versa.

Although they are different effects (strength reduction and maximum hit points reduction), the reasoning for one would apply to the other, given that they are both reductions that end on a long rest. However, I cannot find anything published in their Sage Advice publication to confirm JC's ruling.

Taking from the description of Wild Shape (PHB, pg. 67):

While you are transformed, the following rules apply:

• Your game statistics are replaced by the statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores.

And:

• When you revert to your normal form, you return to the number of hit points you had before you transformed.

That part only discusses hit points reverting back to what you had before, and doesn't explicitly mention your maximum hit points or ability scores returning back to normal, it is only implies by the "While you are transformed" part at the start of this bullet list. Without anything explicit to go on, applying the same reasoning as JC seems consistent with current hit points, at least.

The modifier is directly linked to the stat, so a STR of 19 has a modifier of +4. That just happens automatically. STR based attacks will therefore benefit from the higher modifier. Skill checks will improve if they use the STR modifier as it has improved.

Basically, the modifier instantly increases to match the new total of the stat then that flows over into attack rolls, damage rolls and ability checks/saves that use that modifier.

From the SRD:

When a character makes an attack roll, the two most common modifiers to the roll are an ability modifier and the character's proficiency bonus. When a monster makes an attack roll, it uses whatever modifier is provided in its stat block.

Ability Modifier. The ability modifier used for a melee weapon attack is Strength