I will say that I purposefully didn't read any of the responses because this topic can make me really mad so I apologize in advance if I am duplicating any responses.
I have a 15 month old who is having that exact thing going on. Her eye teeth started to descend and it took me a while to connect the two and I was FRUSTRATED by the fact that she was hungry all of the time but wouldn't eat a darn thing so I feel your pain.
Once I figured out it was her teeth it was a lot easier but finding food she will eat has not gotten any easier. She likes something one minute and is spitting it across the room in another minute. She won't try anything new and foods she loves (normally) she won't touch. I am really grateful that we are still nursing and also very grateful for polenta and thick greek yogurt and honey. That is what she is surviving on right now.
This is my thing about the food. It is virtually impossible to control if a child (particularly a baby) will eat. There are two things that we as parents cannot control--what they will swallow when, and what/when stuff comes out the other end.
These babies aren't even toddlers yet and while they are smart and they are learning things and picking up on things, making an issue over their food, in my opinion, is what will lead to eating troubles later. I kind of view it as the same as when an older child is sick....you feed them whenever they need it and it is usually different than what you are eating. If you have a normal routine, which it sounds like you do, variance from that for a while isn't going to hurt or set off terrible habits, etc. Once the phase (or teething) has passed, you will bring them back around to the way that your family operates and more than likely without any problem.
My sister gave me a tip once that has helped quite a bit lately....take baby washclothes, roll some of them with the fuzzy inward and some with it outward until you know what your child prefers, wet them well but not dripping and put them in the freezer (with or without a bag, your preference). Once they are frozen give one to your little guy and see if he gets relief from that. My daughter's whole demeanor changes when she has one to put on her erupting canines, you can just see how good it feels.
Good luck to you!