Carry on

Yes, wheels and handles have to be included. You measure from the top of the handles (if they protrude out) to the bottom of the wheels.
Also measure the thickness...and if the wheels stick out that way as well, include them.

I haven't flown Ryan Air but I suspect a 22 inch with wheels won't work, as they are purported to be very strict. Hopefully someone with actual experience can weigh in.

For RA you need to measure all 3 dimensions Here is what RA says for its carry-on limits:

"It should weigh no more than 10kg and not exceed the maximum dimensions of 55cm x 40cm x 20cm."

http://www.ryanair.com/en/questions/cabin-baggage-allowance