My suggestion is to try listening and reading as much Greek as possible, until you get an intuitive feeling about how to order the words. Trying to learn a list of words order rules sounds like nightmare...
My teacher has told us in the classes : when we are in doubt about the words order, simply use the romanian words order (this is my native language) and the order will be ok most of the times. I guess that the greek order sounds a bit unnatural for you as english native speaker.
In English the grammar is missing certain features such as declination. This means that the words order can influence a lot the meaning: "the dog eats the cat" vs "the cat eats the dog". The order is the only clue for knowing who is eating whom.
The Greek allows some flexibility : "ο σκύλος τρώει την γάτα " and "την γάτα τρώει ο σκύλος" mean the same thanks to the nouns declinations (the dog is the one who eats the cat in both sentences because ο σκύλος is nominative case and την γάτα is accusative). But I guess that the first sentence is used usually (while the second would be used only when putting extra emphasis the cat is the one who gets eaten, not someone else).