Between what seasons does orbital velocity speed up and slow down?

The season depends on which hemisphere you are in.

The earth's orbit around the sun is not a circle. The earth's orbit around the sun is slightly elliptical. Therefore, the distance between the earth and the sun varies throughout the year.

At its nearest point on the ellipse that is the earth's orbit around the sun, the earth is 91,445,000 miles (147,166,462 km) from the sun. This point in the earth's orbit is known as perihelion and it occurs on January 3. During our closest approach is when our orbital velocity is the greatest.

The earth is farthest away from the sun on July 4 when it is 94,555,000 miles (152,171,522 km) from the sun. This point in the earth's orbit is called aphelion.

The slight ellipse in the earth's orbit does have a slight impact on the amount of solar energy being received by the earth. This 3.3% difference in distance does not impact the earth as much as the seasonal variations, however.

From: http://geography.about.com/od/physicalgeography/a/orbitsun.htm