How do I translate British English strings into US English?
First, I'm not sure about what this means "I cannot see any of the strings from my custom module." ... so my answer here may not be useful.  but here goes: 

Machines don't care about what the similarities are, variations of english might as well be chinese and spanish.. which works in our favour here!

Assuming (US) english is your primary/default language,  translate only the strings you want in to the Queen's English:  admin/config/regional/translate/translate

You may have to do some interesting stuff to make detection/selection work,  but I think that's a new question.