Your skin can be irritated, but not annoyed. Otherwise, they are similar.

Hi,

To my ear, perhaps 'irritated' suggests a shorter duration than 'annoyed', and maybe even a lesser degree of feeling.

Hi,
Thank you both for your reply. According to my dictionary, 'annoy' means to make (someone) a little angry or impatient, esp. by repeated troublesome actions or attacks. Does 'irritate' mean the same as above?

Yes. A person can be irritated by being stuck in traffic, or by an overbearing boss, or by the government's red tape, or many other things.

Your skin can be irritated, too, if you get some strong chemical or fluid on it. It becomes red and prickly.
Your eyes can be irritated by smog - they become watery, red and itchy.

Hi AlpheccaStars,
Thank you for your answer. Would it be the same meaning if I use annoyed in your example here:
A person can be annoyed by being stuck in traffic, or by an overbearing boss, or by the government's red tape, or many other things.

Thanks.

yes.