So, essentially, your damage dealt will be

D = M*T*B*A

Where A is your base damage, D is damage dealt, M is material multiplier, T is damage type multiplier, B is other damage reduction (ABS, sanc etc.) and A is damage dealt before these damage multipliers. Essentially, M is 1 if you aren't vuln/resistant to the material of the weapon hitting you. Similarly, T is 1 if you aren't resistant/vulnerable to the damage type hitting you.

In short, material and damage type behave independently and do not depend on each other in terms of how much damage is dealt. If you are vuln to some material, you are going to take more damage from a weapon made of that material, than from some other weapon with same damage type and a material you are not vuln to.