Both words describe something that causes annoyance or displeasure.
* Irk is a stronger word, implying a sense of being bothered or frustrated.
* Irritate is a more general term, simply meaning to annoy or make someone feel uneasy.
Here's an example to illustrate the difference:
* Irk: "The constant noise from the construction site really irked me." (Stronger annoyance, perhaps bordering on anger)
* Irritate: "The buzzing of the fly irritated her." (Less intense annoyance, more like a mild discomfort)
In most contexts, you can use either word, but "irk" carries a slightly stronger sense of annoyance.