Do neutrons exhibit momentary small charges due to the movement of its quarks? So in a similar way to electrons moving in atoms, causing induced dipole-dipole interactions, can neutrons momentarily attract or repel?
 A: It seems that within the standard model of particle physics 

A permanent electric dipole moment of a fundamental particle violates both parity (P) and time reversal symmetry (T). These violations can be understood by examining the neutron's magnetic dipole moment and hypothetical electric dipole moment. Under time reversal, the magnetic dipole moment changes its direction, whereas the electric dipole moment stays unchanged. Under parity, the electric dipole moment changes its direction but not the magnetic dipole moment. As the resulting system under P and T is not symmetric with respect to the initial system, these symmetries are violated in the case of the existence of an EDM. Having also CPT symmetry, the combined symmetry CP is violated as well.

Thus experiments trying for new physics beyond the standard model have tried to measure it for the neutron:

The neutron electric dipole moment (nEDM) is a measure for the distribution of positive and negative charge inside the neutron. A finite electric dipole moment can only exist if the centers of the negative and positive charge distribution inside the particle do not coincide. So far, no neutron EDM has been found. The current best upper limit amounts to |dn| $< 3.0×10^−26 e⋅cm.$

As CP violation has been observed in particle data,  to a very small amount, the value  due to CP violation for the electric dipole moment of the neutron is expected to be around $ 10^−31 e⋅cm$, way smaller than the present limit.

can neutrons momentarily attract or repel?

Do not forget that the neutrons are in the realm of strong interactions , and will attract other neutrons or protons, in orders of magnitude stronger reaction. The technique for the electric dipole  measurement is described here. 
