They might not have any effects, though some of the respective materials also come with levels of Reinforced.
Thaumic gives one extra modifier for the first part, and another one if the entire tool is made of Thaumium.
Mathematical makes the tool Unbreakable if it is crafted entirely from unstable parts, regardless of levels in Reinforced or final durability.
Heavy might relate to knockback in some way as that is the effect of lead gear in TE. I don't think it's implemented though.
Shiny and Dense at least didn't show any obvious negative effects during regular use.