I have a character with the ability to touch an object and take away its interaction with outside forces such as gravity or pressure. An electric clock for instance would cease functioning because electricity is no longer flowing into the object, but it could get hit by a train and be fine because no force affected the object. So what might some unintended consequences of this be? Would the object even be visible if no light was reflecting off it, or would it be a static image?
Your object would disappear utterly.
For all intents and purposes the object would no longer inhabit our plane of existence. It cannot be said to be "here" in any meaningful sense. It would be imperceptible as it could not be touched, light would not bounce off it to make it visible, gases would not carry away molecules to be smelled, and so on.
And plus, from the perspective of someone who could somehow still see it, it would zoom off into the distance or down into the ground. Taken to its logical extreme this enchanted object would (immediately!) shoot into the universe following the trajectory it had when this spell was put on it. The gravity of the planet and its star would no longer constantly change the direction of the object, and it would go off in a straight line on a tangent to its planet's orbit, possibly traveling through the surface of the planet and back out at some remote site. I cannot think of any way that you could ever find it again.
If you want to have funky bemagickized objects of this sort play a role in the story then you will need to have your protagonist limit the extent of his ensorcellemnt. And then you can have it be what you want. For example, something immune to light but still with mass can still take up space in your pocket and provoke questions from observers. This is pure fantasy but could still be fun.
If it's no longer affected by gravity (but Newton's rules still apply), it will immediately leave Earth; gravity is what keeps Earth in its orbit around the Sun. Right now, the Earth is moving 30 kilometers per second in a direction perpendicular to where the Sun appears to be; that object would continue flying in that direction since there are no forces acting on it.
It will disappear entirety, as light will pass through it. But let's assume you've handwaved a special case for photons. And also handwaved the "launched into space by it's own inertia" problem.
If you've stopped the Electromagnetic forces, (eg stopping the flow of electrons), then you've stopped the ability for the clock to be hit by the train.
The clock will appear to phase through the train, and come out the other side.
Why? Collisions are the electromagnetic force between atoms of two different objects. The atoms of two colliding objects will almost never actually touch each other.
I like my peers view that an object suddenly freed from gravity would fly onto space at great speed in hilarious ways. Let me offer an alter ative scenario though.
Gravity is a force that is proportional to mass, which in very simplified terms comes from the Higgs bosons inside atoms. You can remove all mass from an object by removing those bosons. One such way is to convert them to energy. This will cause a release of energy following that famous equation, $E = mc^2$. There is some conversion here but back of napkin you get the same bang as 21.5 megatons of TNT (about 40%'ish of a Tsar Bomba) per kilogram (~2 pounds).
That would be rude for everybody within a few hundred kilometers of the object (or miles - at this scale it's not much of a difference). As for the object itself, you may be thinking that if it's got no mass AND you make it unable to interact electromagnetically it might just stay intact. Unfortunately, massless particles must all travel at light speed. Which means that despite not being affected by the country-destroying blast you created, the object will be disintegrated because all of its particles will be scattered in random directions at the universe's top speed.
Your spell does not belong in the Alteration or Enchantment schools of magic, it belongs in Destruction.
At a fundamental level, there are only four forces of this universe: Gravitation, Electromagnetism, Strong force and Weak force. How the object is affected depends upon which force is 'cancelled'.
Forget about the weak force; it will have no effect on the object as long as it isn't radioactive. If you turn it off, I think it will remove beta-decay from the object. Any other possible effect, I am not qualified enough to accurately answer. Safe to say this will not play a huge role in the effect (unless you're going reaaaally far into the technicalities.
You also probably do not want to remove the Strong force (Strong Nuclear Force), as otherwise, all the nuclei of all atoms in the object would simultaneously split apart, and, well.... E=mc^2, nuclear hijinks ensue.
Now, for electromagnetism (EM). It is the force responsible for both chemical reactions, and 'contact'. Indeed, atoms are mostly empty space, and when you touch something, you feel something is there because of electromagnetism. Light also reflects off of something because of electromagnetism (it is a wave in the EM field). If you remove the EM force, your object (a clock, in this case) will turn invisible, and it will phase through matter ie it will pass through the moving train unaffected, without collision. Of course no one will care, since no one sees it anyways.
Now for a technicality: Do these forces continue to exist within the object? Or only between the object and the outside world? Because if you remove EM between atoms within the object, it will fall apart into atoms, breaking physical and chemical bonds alike.
(Note that if you take this point, and only take away the forces between the outside and inside, preserving internal forces, then removing the strong interaction and the weak interaction will have no effect whatsoever on the object. They only act internally, so deleting internal-external forces doesn't do anything to them as they were not even present on that scale)
Now, if you preserve internal EM and delete external EM, unless you have some magic to keep the clock in place, it falls towards the centre of the earth, from gravitation.
If you remove gravity, it will not speed off into infinity. Now, assuming you have magic goggles to see it even when EM is removed, you will see it not fall towards the Earth, but hover in place, moving slightly towards the west, because since it is not affected by gravitation, it will not rotate along the Earth.
As to why it doesn't fly off? Well, inertia. When you 'cut the string' of gravity, it still has a velocity equal to that of the Earth. It will slowly move away from the Earth as the Earth revolves, moving (again, slowly) on a path tangent to the Earth's orbit at the point where we switched off gravity, a traveler between the stars, perhaps to be seen again only by aliens if they also possess the magic to see objects who EM has been turned off...