[MagicRat]

CC = cubic centimeter, which is a measurement of volume.
In the case you stated, the combustion chamber volume was being measured. The smaller the chamber, the higher the compression will be. In order to build an engine well, you should measure the combustion chamber volume to determine what type of pistons are required (pop-up, flat top or dished) to achieve a specific compression ratio.

sohc= single overhead camshaft.
This type of engine places the cam in the cylinder head and eliminates the pushrods. This means the valve train has less reciprocating mass allowing the engine to rev higher and produce more power before the valves float.

dohc = double overhead camshaft.
This does the same as sohc, but in this case the intake valves and the exhaust valves each have their own camshafts. This eliminates the valve rocker arms often found in a sohc engine, which makes the valve train even lighter and higher revving. Also, the valves can be placed at a more advantageous angle for even more power.

To summerise, pushrod engines are the cheapest and most compact design, but have the least power.
dohc engines are the most expensive and bulkiest, but produce the most power.
sohc engines are in between.

Finally, these points are very general, and there are lots of exceptions to these points, but you get the idea,