Yes.
Check the prerequisites. Power Attack needs a Strength 13, while Piranha Strike needs Weapon Finess, which is interesting only if your Dex is greater than you Str, so we can deduce that the latter is intended for Dexterity-oriented characters, the fluff text incidentally says one using Piranha Strike provokes "multiple, minor wounds".
For a more complete answer, Power Attack doesn't say anything about light weapons, but it does say that you can use this feat with a natural weapon, and natural weapons are considered light weapons.
Besides, if you couldn't use Power Attack with a light weapon, the description of the Piranha Strike feat wouldn't explicitly tell that
This feat cannot be used in conjunction with the Power Attack feat
The answer to your question is No, using versatile weapons with two hands does not disqualify them as monk weapons.
But not because of any reason that made you ask the question, because your whole question is wrong as it's clear from your question you haven't understood the paragraph in question.
The paragraph in question on pg. 78, PHB says (emphasis mine):
At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.
Let's look at what that paragraph really says.
The first thing it does is stating that at 1st level a monk has a master of different combat styles using unarmed strikes and monk weapons.
The second thing it does is stating that monk weapons are shortswords and any simple melee weapon that doesn't have either the heavy property or the two-handed property.
That's everything that paragraph states. It simply tells you that monks fight unarmed or with monk weapons and then defines monk weapons as either shortswords or any simple melee weapon that isn't heavy or requires two-hands to use.
Simple melee weapon with heavy or two-handed property = not monk weapons.
Simple melee weapon without heavy or two-handed property = monk weapons.
So what about the versatile property? A weapon with that property just gives you the option to use two hands during an attack for greater damage.
However, in this case whether a weapon has the versatile property or not has no impact on the RAW as it only purpose in this case is to define what a monk weapon is, which is a shortsword or any simple melee weapon without either the heavy property or the two-handed property. Any other properties such as light, finesse, reach or versatile has in this case no bearing on the rules. Nor does how you use said weapon.
Best Answer
They would not get the extra fifty percent Str bonus, nor any of the other benefits tied to wielding the weapon with two hands, as you are not. The Two Handed Weapon property means that this weapon usually requires two hands to wield. It is the actual act of wielding a non-light weapon two handed that gives the extra potency behind the swing.
What this Phalanx Fighting (Ex) feature does allow you to do is to have a halberd, longspear, naginata, or what ever your choice of pole arm is in one hand and a spiked shield in the other. Not only does this let you engage at one or two squares away with melee, you cover that much area of attacks of opportunity. This, combined with your ability to shield allies with you features and perhaps teamwork feats, lets you play the sort of defensive fighter that a million Persian can't get passed a scant fifteen score of.