Mob right hand item drop

    @Override
    protected boolean canDropLoot() {
        return false;
    }

Like, on player tick?

use the when mob is hit with tool trigger, and deal extra damage using get global variable

you can add strength potion effect when holding the item

Sorry for the waited response.

add damage to an weapon according to global variable?

For this, do what ShockingArtist said, should work fine.

@ShockingArtist

use the when mob is hit with tool trigger, and deal extra damage using get global variable

For this, just add to the list in the information method....

Would work, but I'd like to have the damage shown in the item

Something like this would work (in addInformation overrides from Item);

list.add(new StringTextComponent("Current Damage: " + WHATEVERGLOBALVARIABLE));

You can add more conditions and such, but that is the basis.