Two things you could do.
#1, open each pc of wood as a part and use the properties function to insert your dim's into, then if you ever change the part it will update your dim's in you BOM.
#2 Is to create the part as a weldment.. you'd need to create a set of library features using the various sizes of wood [ei 2 x 4 but would actually measure 1.5 x 3.5 etc] this would get you part of the job done. You'd still have to link some dimensions to part geometry to make the BOM or cutlist complete.
Someone else might be able to point it out, but I've never been able to make the software automatically generate a BOM of dimensions off of regular shaped parts. I'm not saying it can't do it, I just haven't seen it.. and I've been running the software for over 5 years.
It's powerful, but it's not artificially intelligent..