You can use the -verbose option of the java command and search for the fully qualified name of a specific class.
$ java -verbose -jar MyProgram.jar | grep "java.lang.String"
[Loaded java.lang.String from /Library/Java/…/Contents/Home/jre/lib/rt.jar]
[Loaded java.lang.StringBuffer from /Library/Java/…/Contents/Home/jre/lib/rt.jar]
…
Addendum: I want to check the class availability for an environment.
If you are running from the java command line, either the paths specified in the -classpath option or the CLASSPATH environment variable will be searched. If you are running from a JAR, the manifest's Class-Path attribute, for example, supplants these settings.
If you are trying to find a required JAR that may not be accessible in these ways, you'll have to search the file system. I use a combination of find, jar and grep, typically focussing on paths defined  in system properties such as java.endorsed.dirs and java.ext.dirs; several related approaches are shown here.