Can all fundamental forces be repulsive? If the electric force can be attractive (with opposite charges) or repulsive (same charges), and the magnetic force acts like this too, can all forces be repulsive in some cases? For example, could gravity and the strong force actually repel certain things?
 A: Whether forces can be repulsive or not depends on the spin of their mediating field. A scalar (spin-0) force is universally attractive, as is a spin-2 force, while a spin-1 is attractive for different charges and repulsive for like charges.
So the electromagnetic, the weak and the strong force can be repulsive, while gravity cannot.
A: 
Can all fundamental forces be repulsive?

No. 

If the electric force can be attractive (with opposite charges) or repulsive (same charges), and the magnetic force acts like this too, can all forces be repulsive in some cases?

No. 

For example, could gravity and the strong force actually repel certain things?

The strong force can exhibit repulsion, but gravity doesn't. Remember that light bends downwards in a gravitational field, and we can make both matter and antimatter out of light in pair production. If you had a gedanken box containing an electron, it would have the same mass as another gedanken box containing a positron, and both would behave the same gravitationally. They both fall down. IMHO the best way to appreciate why is to focus on the wave nature of matter, and think of atomic orbitals where "electrons exist as standing waves". Think of the electron as standing wave or matter wave in a closed path. Then the positron, which has the opposite chirality, is in a closed path too, but "going the other way". However they both fall down, because waves curve downward regardless of which way round they go:  

There isn't anything that curves up or falls up. Gravity is attractive.   
