Moment of inertia is not a material property, it is a geometric property. Regardless of the material you are dealing with, a member that is 2" wide by 10" tall in cross section has the same moment of inertia. Therefore, you should use the standard equations for calculating your beam section's moment of inertia.
To address the portion of your question regarding wood's non-isotropic (anisotropic) material properties. The governing wood design codes/standards (National Design Specification, NDS, for Wood Construction in the US) suggest ignoring wood's inherent anisotrpoic nature and to, instead, use a conservatively lower value for these properties. The most applicable of these properties for structural wood design is the modulus of elasticity, values for which are compiled in the supplement to NDS list on a per species basis.
And with respect to "de-rating" the material properties since you are creating a built-up member, no, you should not modify your material properties in any manner. You have not changed your material properties have not changed. Instead, you need to calculate the shear force being transferred between all your members and design your dowel fasteners (nails) or glue appropriately. This is done by calculating the shear flow (q = (VQ)/I).
In summary, you can complete your analysis/design by properly calculating the moment of inertia of your built-up member, using the appropriate material properties, and properly sizing your fasteners.