Googled this, thought I'd add my 2 cents.
The text on Flurry of Blows reads:
"When doing so he may make one additional attack using any combination of unarmed strikes or attacks with a special monk weapon as if using the Two-Weapon Fighting feat."
You are doing it "as if" using two-weapon fighting. You are not actually using two-weapon fighting. There are no "off-hand" attacks. You can make the full flurry with only a single weapon should you so choose, whether that weapon is a one-handed weapon, a two-handed weapon, one side of a double weapon, etc. It sounds like most people are in agreement on this.
To make off hand attacks AT ALL one must declare that he's using two-weapon fighting before attacking. And you can't use two-weapon fighting and flurry of blows at the same time since they are mutually exclusive full-attack actions.
Keep in mind that even if you have a weapon in each hand you can attack with both of them without two-weapon fighting. In the FAQ there's an example of a 6th level fight (6/1 BAB) with a longsword and a mace. As a regular full attack he can longsword/longsword, longsword/mace, mace/longsword, or mace/mace, all at +6/+1. You only incur the two-weapon fighting penalties if you gain the extra attack (or rather, intend to gain it by declaring you are two-weapon fighting at the beginning of the action). The fact that you are using a weapon in each hand doesn't actually matter.
Where I differ with people is in the 1x Str or 1.5x Str discussion. The text states that
"A monk applies his full Strength bonus to his damage rolls for all successful attacks made with flurry of blows, whether the attacks are made with an off-hand or with a weapon wielded in both hands."
Note that it doesn't say "full Strength MODIFIER", it says "full Strength bonus to damage". Well the "strength bonus to damage" is 1.5x Str mod when wielding a weapon with 2 hands and it's 0.5x Str mod for off-hand attacks, although I think we're in agreement that this part is irrelevant because you can't actually make off-hand attacks as part of a flurry. You definitely can make attacks with a two-handed weapon though, so the first part matters.
I do believe the intention was for ALL attacks during a flurry to get the same x1 Str mod to damage, but it's not completely clear that this is the case from the wording. For balance purposes though I enforce this in my own games. Flurry is already powerful enough without adding extra damage.
Edit: Two 2 main questions here (1.5x or 1x and 3x or 2x power attack) shoudl be in the FAQ. If you're reading this and you agree go up to the original post and hit the FAQ button.