I am looking for a list of classes of synthetic organic chemicals. I'm not very strong in chemistry. The only information I could find are from here which seem to describe SOC's are like pesticides or fuel additives, but I don't think you can call those classes.
There are a lot of organic chemicals.
Due to the incomprehensibly vast number of chemical species and variation between them, almost every classification system is domain-specific.
In terms of pure chemistry, the best you can do is usually to organize them according to what functional groups are in play; this will usually reveal something about the fundamental chemical interactions available to the species in question, but this is not necessarily useful or enlightening:
In many applications, such as as antifreeze, fuel or a solvent, methanol and ethanol are (largely) interchangeable: They both have short carbon chains attached to a single alcohol group (-OH), their boiling points, dipole moments, chemical energy and other properties are similar, and they mostly react in the same way on a chemical level.
In other applications, however, they are as night and day: In biology, methanol is a potent poison, and ethanol is a mostly harmless intoxicant.
Organic chemistry is, in short, notoriously resilient to generally useful classification systems.