Ian Keane

You can get a sense of what the names mean by breaking down the Japanese vocabulary:

sho = front
men = head
uchi = strike

So, for example, shomen uchi is a strike at the front of your opponent's head.

hidari = left
migi = right

A kesa is a sash or stole worn by monks, extending from the left shoulder to the right hip. It is used in a metaphorical context here, to indicate a diagonal line from the shoulder to the hip.

giri = cut
ichimonji = a horizontal line

I'm not sure about joho, but it is often attached to the beginning of words to indicate "upward".

age = rising

Hope that helps.