Inputting multiple strings and finding their length

num_of_items = int(input("How many items in your list? "))

For one thing, what if the user typed alpha? You would have a nasty error throwing itself at the user. Why are you asking anyway? You should be able to handle any number of items without asking. Just keep asking input and printing output until the user decides to end with exit. Even as it is, your item_list() function will print only the first four and if num_of_items is, say, three ... IndexError.

num_of_items ...
def item_list(x):
    ...

That's a little squooshed. I would add at least one blank line and probably two between the num_of_items definition and the item_list() definition. Well, actually I would put the num_of_items definition below the function definition. Usually, constants are defined first; then functions and classes; then variables.

item = input("Enter list %r: " % (i+1))

% formatting is not officially deprecated, but it is preferred to use .format()

I wouldn't create a list of strings whose sole purpose is to be displayed to the user. There are some things such as get_accuracy(user) where you might not use it elsewhere, but it makes sense to use it programmatically. In this case, you are returning strings that couldn't be read by your program very easily. Your item_list() function should not return strings that are formatted just for the reader. It should return something that you can format however you like elsewhere. My modified program looks like this:

def get_items():
    while True:
        item = input("Enter string: ")
        if item.lower() == "exit":
            raise StopIteration()
        yield item, len(item)

for item in get_items():
    print("The length of string '{0}' is {1}".format(*item))

get_items() is now a generator function that yields tuples of each item and its length. Since it raises StopIteration when the user types exit, the for loop will stop.

First, I'd like to comment on your formatting and structure. Generally, definitions are placed first in a file. Seeing it right in between two statements is a bit confusing. I'd also put the newline before the def line rather than after, after all the indented block is more related to the definition than the preceding line.

On to your questions. There is a cleaner way to include dynamic strings in string literals: using the format method. This is an example from the documentation:

>>> "The sum of 1 + 2 is {0}".format(1+2)
'The sum of 1 + 2 is 3'

Applying this to your code might look like this:

"The length of '{0}' is {1}".format(items[0], len(items[0]))

Which would yield this, for instance:

The length of string 'Dog' is 3

Right now, the user has to enter at least four strings, or the program will crash. In addition, if the user enters more strings, only the first four are printed. You could improve your algorithm to handle any number of strings using a second loop, or a list comprehension like below.

str_list = ["The length of '{0} is {1}".format(item, len(item)) for item in items]

This line creates a list with one entry per element in items. The equivalent using a for loop would be this:

str_list = []
for item in items:
    str_list.append("The length of '{0} is {1}".format(item, len(item))