Static methods (in fact all methods) as well as static variables are stored in the PermGen section of the heap, since they are part of the reflection data (class related data, not instance related). As of Java 8 PermGen has been replaced by MetaSpace and as per JEP 122 it only holds meta-data while static fields are stored in the heap.
Note that this mostly applies to Oracle’s Hotspot JVM and others that are based on it. However, not every JVM has PermGen or Metaspace like Eclipse OpenJ9.
Update for clarification:
Note that only the variables and their technical values (primitives or references) are stored in PermGen space.
If your static variable is a reference to an object that object itself is stored in the normal sections of the heap (young/old generation or survivor space). Those objects (unless they are internal objects like classes etc.) are not stored in PermGen space.
Example:
static int i = 1; //the value 1 is stored in the PermGen section
static Object o = new SomeObject(); //the reference(pointer/memory address) is stored in the PermGen section, the object itself is not.
A word on garbage collection:
Do not rely on finalize() as it’s not guaranteed to run. It is totally up to the JVM to decide when to run the garbage collector and what to collect, even if an object is eligible for garbage collection.
Of course you can set a static variable to null and thus remove the reference to the object on the heap but that doesn’t mean the garbage collector will collect it (even if there are no more references).
Additionally finalize() is run only once, so you have to make sure it doesn’t throw exceptions or otherwise prevent the object to be collected. If you halt finalization through some exception, finalize() won’t be invoked on the same object a second time.
A final note: how code, runtime data etc. are stored depends on the JVM which is used, i.e. HotSpot might do it differently than JRockit and this might even differ between versions of the same JVM. The above is based on HotSpot for Java 5 and 6 (those are basically the same) since at the time of answering I’d say that most people used those JVMs. Due to major changes in the memory model as of Java 8, the statements above might not be true for Java 8 HotSpot – and I didn’t check the changes of Java 7 HotSpot, so I guess the above is still true for that version, but I’m not sure here.