For example a Water/Flying like Gyarados getting hit by Forest's Curse and becoming a Water/Flying/Grass then getting hit by Freeze-Dry which is Super effective against all of the three types'
Will it become a *8 super effective ?
In the example you gave, yes. Any Pokemon already 4x weak to Freeze-Dry with Forest's Curse used on them will become 8x weak to Freeze-Dry.
Another example would be Palkia with Forest's Curse used on it, or any of the Water/Ground types.
Hope I helped!
Yes, it does. Freeze-dry is 2x effective against water, another 2x against flying (making it 2 x 2 = 4x) and its 2x against grass, meaning its 2 x 2 x 2 = 8x effective.
Yes, it can be 8x effective. Also, Dragon/Water/Grass could be one.