How to handle both integer and string from raw_input?

Let me answer your question with another question:
Is it really necessary to mix letters and numbers?
Can't they just be all strings?

Well, let's take the long way and see what the program is doing:

1. Display the main menu
2. Ask/receive the user input
   • If is valid: ok
   • If not: print an error message and repeat
3. Now we have a valid input
   • If is a letter: do a special tasks
   • If is a number: call the right draw-function

Point 1. Let's make a function for this:

def display_menu():
    menu_text = """\
  Draw a Shape
  ============

  1 - Draw a triangle
  2 - Draw a square
  D - Display what was drawn
  X - Exit"""
    print menu_text

display_menu is very simple so there's no need to explain what it does, but we'll see later the advantage of putting this code into a separate function.

Point 2. This will be done with a loop:

options = ['1', '2', 'D', 'X']

while 1:
    choice = raw_input('  Enter your choice: ')
    if choice in options:
        break
    else:
        print 'Try Again!'

Point 3. Well, after a second thought maybe the special tasks are not so special, so let's put them too into a function:

def exit():
    """Exit"""  # this is a docstring we'll use it later
    return 0

def display_drawn():
    """Display what was drawn"""
    print 'display what was drawn'

def draw_triangle():
    """Draw a triangle"""
    print 'triangle'

def draw_square():
    """Draw a square"""
    print 'square'

Now let's put it all together:

def main():
    options = {'1': draw_triangle,
               '2': draw_square,
               'D': display_drawn,
               'X': exit}

    display_menu()
    while 1:
        choice = raw_input('  Enter your choice: ').upper()
        if choice in options:
            break
        else:
            print 'Try Again!'

    action = options[choice]   # here we get the right function
    action()     # here we call that function

The key to your switch lies in options that now is no more a list but a dict, so if you simply iterate on it like if choice in options your iteration is on the keys:['1', '2', 'D', 'X'], but if you do options['X'] you get the exit function (isn't that wonderful!).

Now let's improve again, because maintaining the main menu message and the options dictionary it's not too good, a year from now I may forget to change one or the other, I will not get what I want and I'm lazy and I don't want to do twice the same thing, etc...
So why don't pass the options dictionary to display_manu and let display_menu do all the work using the doc-strings in __doc__ to generate the menu:

def display_menu(opt):
    header = """\
  Draw a Shape
  ============

"""
    menu = '\n'.join('{} - {}'.format(k,func.__doc__) for k,func in opt.items())
    print header + menu

We'll need OrderedDict instead of dict for options, because OrderedDict as the name suggests keep the order of its items (take a look at the official doc). So we have:

def main():
    options = OrderedDict((('1', draw_triangle),
                           ('2', draw_square),
                           ('D', display_drawn),
                           ('X', exit)))

    display_menu(options)
    while 1:
        choice = raw_input('  Enter your choice: ').upper()
        if choice in options:
            break
        else:
            print 'Try Again!'

    action = options[choice]
    action()

Beware that you have to design your actions so that they all have the same signature (they should be like that anyway, they are all actions!). You may want to use callables as actions: instances of class with __call__ implemented. Creating a base Action class and inherit from it will be perfect here.