Doubt on genomic code for nucleosome positioning?
Dyad is the centre of the DNA that is wrapped around the nucleosome core (It basically is the centre of symmetry of the nucleosome). It is a common practice to set it at 0 thereby making incoming DNA half, negative and outgoing DNA half, positive.

By oscillations the authors mean that there is a periodic repeat of A/T dinucleotide. IMO it is actually not correct to call it oscillation which is mostly used in a time course dynamical sense. 

I guess this is what is meant by the 3-nt moving average:

You have conditional dinucleotide probabilities for each position (As shown in the figure). Now you calculate the A/T dinucleotide probability which is:  P[A/T] = PAA + PAT + PTT + PTA

Now you find the moving average for 3 steps:

MA(n) = (1/3)×(P[A/T](n) + P[A/T](n-1) + P[A/T](n-2))

where n is the nth position of the DNA