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Basically, what would be the effectiveness of each type on a Pokemon that was Normal, Fire, Water, Grass, Fighting, Electric, Bug, Psychic, Ground, Rock, Dark, Poison, Flying, Steel, Ghost, Ice, Dragon, and Fairy type? (Assuming two times resisted is 1/4, three times resisted is 1/8, four times resisted is 1/16, etc. and 4 times, 8 times, and 16 times for effectiveness respectively).

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Normal: No effect
Fire: Normal effectiveness
Water: Normal effectiveness
Grass: 1/16 damage (4 times resisted.)
Electric: No effect
Ice: Normal effectiveness
Fighting: No effect
Poison: No effect
Ground: No effect
Flying: Normal effectiveness
Psychic: No effect
Bug: 1/16 damage (4 times resisted.)
Rock: 2 times effective (Super Effective)
Ghost: No effect
Dragon: No effect
Dark: 1/2 damage (Resisted one time.)
Steel: 1/2 damage (Resisted one time.)
Fairy: Normal effectiveness.

Source
Me checking every type's attack pros & cons on Pokemon database's type chart. (If anything here is wrong, I blame the fact that I did this at almost 1 in the morning.)

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it must have took long time for you.
Eh not really.
You go to the Dual type charts tab under Game Mechanics. Then, you "add" up the type effectiveness from each type. Easiest way to do this is to go under the Normal/- Type section and click Show All.
If a Pokémon with every type had Flash Fire, Water Absorb/Storm Drain, Volt Absorb/Lightning Rod/Motor Drive, Sap Sipper, Thick Fat, Levitate, Filter, and Solid Rock...its type defense chart would look something like this:

Normal: 0
Fire: 0
Water: 0
Electric: 0
Grass: 0
Ice: (1/2)
Fighting: 0
Poison: 0
Ground: 0
Flying: 1
Psychic: 0
Bug: (1/16)
Rock: (1 1/8) or (9/8)
Ghost: 0
Dragon: 0
Dark: (1/2)
Steel: (1/2)
Fairy: 1