Overall conclusion:

Each type of elemental buff or transform or consumable simply adds a flag for having that damage type.

This flag makes elemental resistances apply to all of your damage except the part added by the buffs/transforms/consumables.

So if you have 100 attack, an enemy has 20% resistance against on it and a buff adds 20% of base attack

the calculation goes (100 x 0.8) + (100 x0.2) which results in no damage difference to unbuffed.

Similarily if you use 2 elemental buffs with one being 40% resist and one being 0% the resulting damage will be the same as with no buffs.

(100 x 0.6) + (100 x (0.2+0.2) = 100

Since cartridges add only 5% of base attack as extra damage a damage loss can be observed in the same cases.

It also means that against only 10% elemental resistance a damage increase could still be observed with the matching buff.

(but only 1 boss has 10% resistance. others generally have 20% atleast)

Lastly, all of the damage including the addition from transformation/buffs/consumables is subject to physical resistances.

So calculations for damage go

1. Multiply base damage by each elemental resist/weakness for which you have a flag for.

2. Add 20% of base damage for each elemental weapon buff/transformation and 5% for each cartridge

3. Multiply the result with physical resistance/weakness (adjust physical resistance value if using merciless reaper)

100 base dmg of slash type, with 4 elemental weapon buffs against an enemy with 20% blood, 40% ice, -10% fire, 0% lightning and 20% slash resistance.

first add the elemental resistances together.

20 + 40 -10 +0 = 50

now multiply that with the base dmg

add the elemental buffs together

0.2 + 0.2 +0.2 +0.2 = 0.8

multiply with base damage

add together both resulting values, then multiply them with the physical resistance

(50 +80) x 0.8 = 104

Let's showcase this on an actual ingame example

Demeter Code, lvl300, dex/fort, fort, mind/fort passives (to meet some requirements)

Argent Wolf King's Blade +10 with a Fire Transformation and Noble Silver +10 with Fortifcation transformation

Base attack value of 1435 and 1477 light gift

Going to test a hit on the dummy in the training area. Which has 0% Frost, -10% Fire/lightning and -30% blood resistance as well as -10% slash resistance

Using the following buffs: Bridge to Glory, Flashing fang, Merciless Reaper, Overdrive, Flame Weapon, Frost Weapon, Lightning Weapon and a Blood cartridge

First lets calculate the basic attack value we get from these buffs.

Flashing fang increases attack by +100% and overdrive increases attack by +25% (both are multiplicative)

So 1435 attack x 2 x 1.25 = 3587.5

(the game doesnt show decimals so it will show a rounded value. i will just keep it as it, as without actually checking it's hard to find out how it rounded.)

Bridge to glory adds 0.5 attack per 1 light we have

0.5 x 1477 +3587.5 = 738.5 + 3587.5 = 4326

So thats our new base attack value. Now lets go into elemental resist calculations for the resulting damage.

We have fire, frost, lightning and blood flags on our damage.

0 - 10 - 10 - 30 = -50 aka a 1.5x multiplier

4326 x 1.5 = 6489

The next step is adding the damage bonus from transform, elemental buffs and cartridge.

Transform adds 20%, each elemental buff adds 20% and cartridge adds 5% (all are additive)

so we take our base attack of 4326 and multiply with (0.2+0.2+0.2+0.2+0.05)

4326 x 0.85 = 3677.1 and add that together with our previous damage value of 6489

3677.1 + 6489 = 10166.1

Lastly, we have our -10% slash resistance to calculate. Since Merciless reaper increases negative physical resistance by x4 that means we have a -40% aka x1.4 multiplier

10166.1 x 1.4 = 14232.54

And here's the actual value we get ingame compared to this calculation