You cannot do much on the client side — you cannot expect the client to have these libraries, and there is no safe way to download and run them.
The easiest way is to write your server side in any way and access them through the web interface. Many languages commonly used for server-side scripting can access native C libraries, or you can even write regular C applications and run them as script agents.
In the "truly exotic" category, you can run what starts with C code in the client if you insert it into a fairly secure environment. For example, see a description of how sqlite (a C database application) was turned into a 100% pure Java application embedding a mips simulator written in java.
http://blog.benad.me/2008/1/22/nestedvm-compile-almost-anything-to-java.html
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