No, you will not get instance-level (classes are not GC-d) information out of a JVM via logging, there is no such setting for that.
The only good option to gain some insight into how GC is performing against instances of a specific class is to take memory dumps and compare them. This way you can spot huge number of instances from a specific class retained. (for example you are accidentally keeping references to a set of streamed objects)
UPDATE:
Since you mentioned that you have many threads, a bit more info on that. Thread-stack only contains local primitives, not object references. So it is very likely that you would find your overflowing objects in the heapdump. If you really believe that your problem is caused by the sheer number of your threads, that you need start configuring the the allowed stack size by using the -Xss option. Since this memory gets reserved even if not used by the thread, you might run out of memory just by spawning too many threads.