Thorough though Thoreau threw, Troll throws through tough troughs
CJam, 11 9 7 bytes

q1b2+B%


How it works:

We are making use of the fact that the sum of the ASCII codes + 2 moded with 11 gives very nice order of 1 through 9 and then 10 for the nine concerned words. Here is the ordering:

through -&gt; 1
thorough -&gt; 2 
tough -&gt; 3 
Thoreau -&gt; 4 
throw -&gt; 5 
threw -&gt; 6 
trough -&gt; 7 
though -&gt; 8 
troll -&gt; 9


Code explanation:

q               e# Read the input
 1b             e# Sum the ASCII code values of all characters in this word
   2+           e# Increment the sum by 2
     B%         e# Mod by 11 and automatically print the mod result at the end


4 bytes saved thanks to user23013

Try it online here