Any list of Irish writers has to include James Joyce. All of his works are set in Ireland. You might want to start with his book Dubliners, which is a collection of short stories. If you're ambitious, you might try to read his novels Ulysses.
Frank McCourt, author of Angela's Ashes and 'Tis, lives in the United States now, but he is from Ireland and has written about his early life and family there.
Maeve Binchey, on the lighter side of literature, has set several of her novels in Ireland, particularly Circle of Friends.
There are many other famous Irish writers, like Seamus Heaney, Samuel Beckett, Jonathon Swift, George Bernard Shaw, and William Butler Yeats. However, they weren't necessarily novelists or, if they were, set their stories in Ireland.
As for etexts, you can find all of the books I've suggested at Amazon or Barnes and Noble. I don't think you're going to find free versions of complete texts anywhere on the internet; although some of Joyce's stories from Dubliners are available. I've provided enotes links to a couple of them and to Joyce's biographical novel Portrait of the Arist as a Young Man.