It seems that they can all mean "easily provoked to anger"
irascible：Easily provoked to outbursts of anger; irritable.
fractious：Irritable; argumentative; quarrelsome.
irritable：1.Capable of being irritated. 2.Easily exasperated or excited.
atrabilious：1.Characterized by melancholy. 2.ill-natured; malevolent.
Best Answer
irritable: On the verge of anger or frustration - usually used when the condition is relatively temporary or short-lived. Ex: "She's very irritable, it must be that time of the month."
irascible: Argumentative, curmudgeonly - Describes a more permanent character flaw. Ex: "I won't shop there anymore, the owner is irascible."
fractious: Someone who seems to be argumentative because they thrive on discord - a "shit-stirrer". Ex: "Sure, go ahead... Invite Marge to be on the committee - all committees need a fractious element."
atrabilious: Don't know. Never heard it. Never read it. Pretty sure it wasn't on the SATs.