Decipher a Code Stick
Python - 219 178 172 175

First crack at it.  I'm sure there's room for improvement.

edit1: After suggestions, and copying words file to local file named 'w'
edit2: Fixed a bug where it wasn't using the right number of letters per side.  Added 3 chars :(

r=range 
s=raw_input()
print[a for a in(''.join(s[m:m+n]for m in r(o*n,len(s),4*n))for o in r(4)for n in(1,2,4,6,8))if not set(a.lower().split())-set(map(str.strip,open('w')))]