Bohemyth is a bi-weekly online journal run by a team based in Dublin. It is described at the website here and has an open submission policy, so there are normally no deadlines. It publishes short stories (max 2,500) and flash fiction (max 700) see here for submission policy.
They are currently looking for submissions for a special Oscar Wilde themed issue - short stories, flash, one act plays and photography. See here for more details. For this themed issue there is a deadline of the end of September.