Java ExecutorService pause/resume a specific thread

You are on the wrong track. The thread pool owns the threads and by sharing them with your code could mess things up.
You should focus on making your tasks (passed to the threads cancellable/interruptable) and not interact with the threads owned by the pool directly.
Additionally you would not know what job is being executed at the time you try to interrupt the thread, so I can't see why you would be interested in doing this

Update:
The proper way to cancel your task submitted in the thread pool is via the Future for the task returned by the executor.
1)This way you know for sure that the task you actually aim at is attempted to be cancelled
2)If your tasks are already designed to be cancellable then your are half way there
3) Do not use a flag to indicate cancellation but use Thread.currentThread().interrupt() instead

Update:

public class InterruptableTasks {  

    private static class InterruptableTask implements Runnable{  
        Object o = new Object();  
        private volatile boolean suspended = false;  

        public void suspend(){          
            suspended = true;  
        }  

        public void resume(){       
            suspended = false;  
            synchronized (o) {  
                o.notifyAll();  
            }  
        }  


        @Override  
        public void run() {  

            while(!Thread.currentThread().isInterrupted()){  
                if(!suspended){  
                    //Do work here      
                }
                else{  
                    //Has been suspended  
                    try {                   
                        while(suspended){  
                            synchronized(o){  
                                o.wait();  
                            }                           
                        }                       
                    }  
                    catch (InterruptedException e) {                    
                    }             
                }                           
            }  
            System.out.println("Cancelled");        
        }

    }

    /**  
     * @param args  
     * @throws InterruptedException   
     */  
    public static void main(String[] args) throws InterruptedException {  
        ExecutorService threadPool = Executors.newCachedThreadPool();  
        InterruptableTask task = new InterruptableTask();  
        Map<Integer, InterruptableTask> tasks = new HashMap<Integer, InterruptableTask>();  
        tasks.put(1, task);  
        //add the tasks and their ids

        Future<?> f = threadPool.submit(task);  
        TimeUnit.SECONDS.sleep(2);  
        InterruptableTask theTask = tasks.get(1);//get task by id
        theTask.suspend();  
        TimeUnit.SECONDS.sleep(2);  
        theTask.resume();  
        TimeUnit.SECONDS.sleep(4);                
        threadPool.shutdownNow();      
    }

Suggestion: Similarly to/instead of the flags you're using, create a semaphore with 1 permit (new Semaphore(1)) for each task you need to pause/unpause. At the beginning of the task's working cycle put a code like this:

semaphore.acquire();
semaphore.release();

This causes the task to acquire a semaphore permit and immediately release it. Now if you want to pause the thread (a button is pressed, for example), call semaphore.acquire() from another thread. Since the semaphore has 0 permits now, your working thread will pause at the beginning of the next cycle and wait until you call semaphore.release() from the other thread.

(The acquire() method throws InterruptedException, if your working thread gets interrupted while waiting. There is another method acquireUninterruptibly(), which also tries to acquire a permit, but doesn't get interrupted.)