This exception is thrown when you try to call wait()/notify()/notifyAll() any of these methods for an Object from a point in your program where u are NOT having a lock on that object.(i.e. u r not executing any synchronized block/method of that object and still trying to call wait()/notify()/notifyAll()) wait(), notify() and notifyAll() all throw IllegalMonitorStateException. since This exception is a subclass of RuntimeException so we r not bound to catch it (although u may if u want to). and being a RuntimeException this exception is not mentioned in the signature of wait(), notify(), notifyAll() methods.
Thread.sleep() takes the current thread to a "Not Runnable" state for specified amount of time. The thread holds the monitors it has acquired. For example, if a thread is running a synchronized block or method and sleep method is called then no other thread will be able to enter this block or method. The sleeping thread can wake up when some other thread calls t.interrupt on it. Note that sleep is a static method, that means it always affects the current thread (the one executing sleep method). A common mistake is trying to call t2.sleep() where t2 is a different thread; even then, it is the current thread that will sleep, not the t2 thread. thread.suspend() is deprecated method. Its possible to send other threads into suspended state by making a suspend method call. In suspended state a thread keeps all its monitors and can not be interrupted. This may cause deadlocks therefore it has been deprecated. object.wait() call also takes the current thread into a "Not Runnable" state, just like sleep(), but with a slight change. Wait method is invoked on a lock object, not thread.
Here is the sequence of operations you can think
Synchronized static methods have a lock on the class "Class", so when a thread enters a synchronized static method, the class itself gets locked by the thread monitor and no other thread can enter any static synchronized methods on that class. This is unlike instance methods, as multiple threads can access "same synchronized instance methods" at same time for different instances.