They say a picture is worth a thousand words.....so how about 2 pictures?
The arrow with the red fletching shows the feathers put on with an offset. Notice how the feather is not perfectly parallel to the arrow shaft but sits at a slight angle.
The arrow with the pink fletch shows feathers with helical (actually it is both offset and helical). The feather is sort of wrapped around the shaft giving the feather a sort of "S" look.
A straight fletch generally means the fletching is directly centerline on the arrow shaft and is parallel to the shaft. Generally straight fletch is used only for target shooting and field tipped arrows.
Offset fletching is probably the most common. It provides more drag and thus more stabilization than a straight fletch.
Helical will give you the best stability performance, however it will tend to loose speed faster downrange (>35-40 yards) due to the increased drag.
As far as right or left offset or helical, you can shoot either. The distinction for right and left helical comes from recurve shooters. If you were right handed, you wanted left helical so that on the shot the arrow would rotate left and away from the arrow shelf. The opposite for a left handed shooter. With modern compounds it makes no difference.
Some will tell you that you should shoot right offset/helical so that the spinning action will tighten your tip/broadhead as oppsosed to loosen it. This might be the case if your tips are finger tight, but any properly torqued broadhead or fieldpoint will not come loose regardless of how fast you spin the arrow.
Hope this helps.