Speed, velocity, and momentum of light As far as I understand speed is a rate of travel and velocity is a directional rate of travel.
The equation for momentum is given as follows $$p=mv$$
Where $m$ is mass and $v$ is velocity.
Case 1. Suppose a photon of light is traveling along the $x$ axis, parallel to the path of travel but not along it is a super massive object that bends the path of light.  The object loses velocity in the $x$ direction but gains velocity towards the object in the $-y$ direction.  In this case, it seems that momentum is converted from $x$ to $-y$ because of the external force.  Normally an object would speed up from an external force acting perpendicular to it, but light doesn't.
Case 2.  Same scenario except the super massive object is in the path of the photon.  Now the photon is traveling into the gravitational field.  The light does not speed up though because the speed of light is constant.  
My question in both cases is, what happens to the extra energy?
 A: *

*As you say, spacetime will be bent by the stress-energy (mass) of the super massive object. Light will travel along the bent path, it's speed will be still constant c when measured locally. (when measured by a far away observer, who is in a weaker gravitational field, speed of light will be less then c)
Let's say the photon does not travel in expanding space in this case, and is not getting red/blueshifted. And let's say it's frequency will not change.
In this case the photon will not gain extra energy, it's energy comes from E=h*f. 
Now I was not talking about momentum change here.
To the comments, to a local observer, if the momentum of the photon would change, then yes, the energy would change too, since to a local observer, speed if light is constant. But to a far away observer, speed of light will be less then c, and so the momentum can change without change of energy.

*Again, the speed of light will be constant to a local observer, but not to a far away observer. Let's say to a local observer the photon will not change it's frequency either (no red/blueshift). 
In this case to a local observer will see momentum change as change of energy, since speed of light is constant. Again, to a far away observer, this is not true, since speed of light might be less then c and so momentum change can happen without change of energy.
