I am creating a virtual solar system model and I want it to be as realistic as possible (e.g. orbits are ellipses, not circles, and orbits are oriented correctly, not all coplanar). In order for me to do this, I need to know the eccentricity of the orbit, the perihelion, the semi-major-axis, inclination and azimuth. I have all of this information, except for the azimuth of the orbit, which is the angle from the sun to the aphelion. Are there any reliable sources with this information?
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)
The Keplerian elements for the planets provides all of the information needed to define the orbit and where the planet is currently along it.
Approximate elements are available from JPL and can be found here: http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt
If you don't want to do the math, you can just ask JPL Horizons to do it for you and calculate an ephemeris telling you which direction each planet is in right now: http://ssd.jpl.nasa.gov/horizons.cgi