What are the azimuths of the planets' orbits?
As someone commented, you are actually short a term for fully defining the orbit.  The "azimuth" as you describe is commonly defined as a "longitude of perihelion", and you're forgetting the orientation of the inclination, commonly defined as "longitude of the ascending node." (Both of these values are included in the first link in the previous posted answer) 

For a more detailed look at the math which uses the defining values, JPL made a whitepaper which goes into the math, and also allows you to account for changes in the orbital terms.  (Most of the math you're probably looking for is at the end of the document, beginning about section 8.10, on page 25)

ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/ExplSupplChap8.pdf