Basically, a monk is allowed to fight with two weapons as if his flurry of blows were his regular primary attack routine. This means that the flurry penalty, if any (-2, -1, or -0) stacks with whatever two-weapon fighting penalty you're taking (-4/-4 or -2/-2, if you have the 2WF feat), and you get the usual one off-hand attack (or 2 off-hand attacks with Improved 2WF, or 3 off-hand attacks with Greater 2WF). These off-hand attacks aren't flurry attacks, so you can use any weapon to make them, but you cannot freely interchange weapons with your off-hand like you can with the flurry.
The monk's primary attacks get x1 the Str bonus to damage, and off-hand attacks (even if they're made with unarmed strikes) get x0.5 the Str bonus to damage, just like any other form of two-weapon fighting. The text in the PHB that says there's no such thing as an off-hand for a monk striking unarmed only refers to the fact that monks are perfectly ambidextrous, and can make primary hand unarmed strikes with any part of the body -- it does not disallow off-hand unarmed strikes, or give them any special bonus (like full Str damage) when they make such attacks.
Keep in mind that when you flurry and fight with two weapons, you must still keep your "hands" separate. Any special monk weapon that used in your flurry routine may not be your off-hand attack, and if your off-hand attack is made with a special monk weapon, you cannot include that wepaon in your flurry. Likewise, even though a monk can use any part of his body to make an unarmed strike, you cannot use the same body part to make unarmed strikes with both your primary "hand" and your off "hand" -- which doesn't actually mean anything in terms of game statstics, unless you've had one of your limbs enhanced with magic weapon or magic fang, because then you only get the enahncement bonus to one of your "hands" (you have to recieve the spell twice to get the bonus to each "hand".)
The maximum possible numeber of attacks goes to the epic-level fighter5/monk17 with the Perfect Two-Weapon Fighting feat. Flurry bonus of +17/+17/+17/+12/+7/+2, and P2WF says that you make as many off-hand attacks as your primary attack bonus -- that's a full attack of +15/+15/+15/+15/+15/+15/+10/+10/+5/+5/+0/+0, without even resorting to haste (to do this, though, you have to assume that P2WF lets you flurry in your off-hand at the same time you flurry with your main hand -- you still have to keep weapons separate to each routine, but all your attacks must be made with UA strikes or SM weapons, and you can change up different weapons, so long as they stay in only one "hand"). Note that this only looks sick and unbalanced, until you realize that a straight fighter or ranger will have fewer dice to roll, but a much better chance of connecting with any given attack.