Can energy only be transferred if there is motion.

[Berney123]

For example if I punch an object and it doesn't move, am I giving it energy, if so after doing that billions of times wouldn't it gain mass because e=mc2.

 

[mfb]

For example if I punch an object and it doesn't move, am I giving it energy

You are not. The Earth (or whatever prevents the object from moving) pushes against the object in the opposite direction, and the energy gained by the object is 0. If you take deformations into account, you could heat it a tiny bit, but that is not related to the motion of the whole object.

 

[Boy@n]

For example if I punch an object and it doesn't move, am I giving it energy, if so after doing that billions of times wouldn't it gain mass because e=mc2.

Depends I guess. If you are hammering iron to make a sword you transfer quite a lot of energy into unmovable object.

 

[FireStorm000]

Kinetic energy is directly tied to motion, so in that sense, no. However, there are many other types of energy, such as the deformation that has already been alluded to. When you punch a box or you hit a sword with a hammer, however, the give the slightest amount, and in that moment apply a great deal of force, absorbing energy in the form of heat and deformation. The kinetic energy of the object as a whole doesn't change though.