T-cell migration to the brain is very limited and occurs at a very low level in healthy conditions, however during diseases the number of T cells passing through the blood-brain barrier is elevate due to increased expression of traffic signals and adhesive molecules.
I've found two good articles on how T-cells migrate through blood-brain barrier:
J Neural Transm (2006) 113: 477–485
Molecular mechanisms involved in T cell migration across
the blood–brain barrier, B. Engelhardt
D. W. Miller, “Immunobiology of the blood-brain barrier.,” J. Neurovirol., vol. 5, no. 6, pp. 570–578, 1999.
During T-cell maturation, those that react too heavily to antigens of the body are killed to avoid having T-cells that would kill the body's own cells. But in rare cases this process fails and auto-reactive T-cell get released from the thymus (This short paper is good for starters). So the (simplified) reason why T-cells attack oligodendrocytes is that they falsely recognize them as pathogens, and therefore kill them. The loss of oligodendrocytes results in loss of myelin sheats.
Also in this paper (it holds many info on demyelination and multiple sclerosis) it is shown that even non-specicfic T-cells can open the way for antibodies through the blood-brain barried, and this results in extended demyelination.