You can access OGo services using XML-RPC from ANSI-C. On the other side you might consider learning ObjC (~1 day task for a developer fluent in C) and get access to the full OGo environment.
In addition its easy to wrap OGo Objective-C classes in ANSI-C APIs in case you are restricted to use "pure" C.

A very simple example for accessing OpenGroupware.org appointment information is available in c_sample.