Can we call a "case" inside another case in the same switch statement in Java?

You can't just call a another case block like this. What you could do, though, is wrap each of these blocks in a method, and reuse them:

private void doSomething() {
    // implementation
}

private void doSomethingElse() {
    // implementation
}

private void runSwitch(int order) {

    switch (orderType) {
           case 1: 
                doSomething();
                break;
           case 2:
                doSomethingElse();
                break;
           case 3:
                doSomething();
                doSomethingElse();
                break;
           default:
                break;
    }
}

Although you cannot influence the switch cases directly, you can call switch's parent method from one case and pass different arguments. For example,

void foo(int param1, String param2, ...) {
    switch (param1) {
        case 0:
            foo(1, "some string");
            break;

        case 1:
            //do something
            break;

        default:
            break;
    }
}

No, you can't jump to the code snippet in another switch case. You can however extract the code into an own method that can be called from another case:

switch (orderType) {
    case 1: 
        someMethod1();
        break;
    case 2:
        someMethod2();
        break;
    case 3:
        someMethod1();
        someMethod2();
        break;
    default:
        break;
}

void someMethod1() { ... }
void someMethod2() { ... }